AP Calculus BC Flashcards: Harmonic Series And P Series

Study Harmonic Series And P Series in AP Calculus BC with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Calculus BC

Harmonic Series And P Series

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QUESTION

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What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{0.3}}$ ?

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ANSWER

p-series. Has form $\sum \frac{1}{n^p}$ with $p = 0.3$ .

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What this deck covers

This deck focuses on Harmonic Series And P Series, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus BC.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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Flashcard 1: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{0.3}}$ ?

Answer: p-series. Has form $\sum \frac{1}{n^p}$ with $p = 0.3$ .

Flashcard 2: What is the condition for the convergence of a harmonic series?

Answer: Always diverges. The harmonic series is famously always divergent.

Flashcard 3: Does the series $\sum_{n=1}^{\infty} \frac{1}{n}$ converge or diverge?

Answer: Diverges. The harmonic series is the classic divergent series.

Flashcard 4: Identify the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^2}$ .

Answer: Converges. Since $p = 2 > 1$ , this p-series converges.

Flashcard 5: Is $\sum_{n=1}^{\infty} \frac{1}{n^{0.5}}$ convergent or divergent?

Answer: Divergent. Since $p = 0.5 \leq 1$ , this p-series diverges.

Flashcard 6: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ ?

Answer: p-series. Has the form $\sum \frac{1}{n^p}$ with $p = 1.5$ .

Flashcard 7: What is the nature of $\sum_{n=1}^{\infty} \frac{1}{n^{2.1}}$ ?

Answer: Convergent. Since $p = 2.1 > 1$ , this p-series converges.

Flashcard 8: What is the fifth term of a harmonic series?

Answer: $\frac{1}{5}$ . The fifth term in the harmonic series is $\frac{1}{5}$ .

Flashcard 9: Does the series $\sum_{n=1}^{\infty} \frac{1}{n}$ converge or diverge?

Answer: Diverges. The harmonic series is the classic divergent series.

Flashcard 10: Identify the series that converges: $\sum_{n=1}^{\infty} \frac{1}{n^3}$ or $\sum_{n=1}^{\infty} \frac{1}{n}$ .

Answer: $\sum_{n=1}^{\infty} \frac{1}{n^3}$ . Since $p = 3 > 1$ , the first series converges.

Flashcard 11: Identify if $\sum_{n=1}^{\infty} \frac{1}{n^{1/2}}$ converges or diverges.

Answer: Diverges. Since $p = 0.5 < 1$ , this p-series diverges.

Flashcard 12: For which values of $p$ does $\sum_{n=1}^{\infty} \frac{1}{n^p}$ diverge?

Answer: $p \leq 1$ . P-series diverge when $p$ is at most 1.

Flashcard 13: What is the condition for the convergence of a harmonic series?

Answer: Always diverges. The harmonic series is famously always divergent.

Flashcard 14: What is the fourth term of a harmonic series?

Answer: $\frac{1}{4}$ . The fourth term in the harmonic series is $\frac{1}{4}$ .

Flashcard 15: Does the series $\sum_{n=1}^{\infty} \frac{1}{n^{3.5}}$ converge?

Answer: Converges. Since $p = 3.5 > 1$ , this p-series converges.

Flashcard 16: State the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{0.8}}$ .

Answer: Diverges. Since $p = 0.8 < 1$ , this p-series diverges.

Flashcard 17: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{0.6}}$ is convergent.

Answer: Diverges. Since $p = 0.6 < 1$ , this p-series diverges.

Flashcard 18: What condition makes a p-series converge?

Answer: Converges if $p > 1$ . When $p > 1$ , the terms decrease fast enough for convergence.

Flashcard 19: Identify the type of series: $\sum_{n=1}^{\infty} \frac{1}{n^{0.9}}$ .

Answer: p-series. Has form $\sum \frac{1}{n^p}$ with $p = 0.9$ .

Flashcard 20: What is the second term of a harmonic series?

Answer: $\frac{1}{2}$ . The second term in the harmonic series is $\frac{1}{2}$ .

Flashcard 21: For which $p$ is the series $\sum_{n=1}^{\infty} \frac{1}{n^p}$ divergent?

Answer: $p \leq 1$ . P-series diverge when $p$ is at most 1.

Flashcard 22: Does $\sum_{n=1}^{\infty} \frac{1}{n^{0.7}}$ converge or diverge?

Answer: Diverges. Since $p = 0.7 < 1$ , this p-series diverges.

Flashcard 23: Determine the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{4}}$ .

Answer: Converges. Since $p = 4 > 1$ , this p-series converges.

Flashcard 24: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{0.6}}$ is convergent.

Answer: Diverges. Since $p = 0.6 < 1$ , this p-series diverges.

Flashcard 25: Identify the series that converges: $\sum_{n=1}^{\infty} \frac{1}{n^3}$ or $\sum_{n=1}^{\infty} \frac{1}{n}$ .

Answer: $\sum_{n=1}^{\infty} \frac{1}{n^3}$ . Since $p = 3 > 1$ , the first series converges.

Flashcard 26: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ converges.

Answer: Converges. Since $p = 1.5 > 1$ , this p-series converges.

Flashcard 27: Identify if $\sum_{n=1}^{\infty} \frac{1}{n^{3/2}}$ converges or diverges.

Answer: Converges. Since $p = 1.5 > 1$ , this p-series converges.

Flashcard 28: What is the definition of a harmonic series?

Answer: The series $\sum_{n=1}^{\infty} \frac{1}{n}$ . The classic divergent series with terms $\frac{1}{n}$ .

Flashcard 29: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ converges.

Answer: Converges. Since $p = 1.5 > 1$ , this p-series converges.

Flashcard 30: Which series is divergent: $\sum_{n=1}^{\infty} \frac{1}{n}$ or $\sum_{n=1}^{\infty} \frac{1}{n^2}$ ?

Answer: $\sum_{n=1}^{\infty} \frac{1}{n}$ . The harmonic series diverges while $\sum \frac{1}{n^2}$ converges.

Flashcard 31: What is the third term of a harmonic series?

Answer: $\frac{1}{3}$ . The third term in the harmonic series is $\frac{1}{3}$ .

Flashcard 32: Identify the type of series: $\sum_{n=1}^{\infty} \frac{1}{n^{0.9}}$ .

Answer: p-series. Has form $\sum \frac{1}{n^p}$ with $p = 0.9$ .

Flashcard 33: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ ?

Answer: p-series. Has the form $\sum \frac{1}{n^p}$ with $p = 1.5$ .

Flashcard 34: What condition makes a p-series diverge?

Answer: Diverges if $p \leq 1$ . When $p \leq 1$ , terms don't decrease fast enough.

Flashcard 35: What is the fourth term of a harmonic series?

Answer: $\frac{1}{4}$ . The fourth term in the harmonic series is $\frac{1}{4}$ .

Flashcard 36: State the formula for a p-series.

Answer: $\sum_{n=1}^{\infty} \frac{1}{n^p}$ . General form where $p$ determines convergence behavior.

Flashcard 37: What is the definition of a harmonic series?

Answer: The series $\sum_{n=1}^{\infty} \frac{1}{n}$ . The classic divergent series with terms $\frac{1}{n}$ .

Flashcard 38: What is the fifth term of a harmonic series?

Answer: $\frac{1}{5}$ . The fifth term in the harmonic series is $\frac{1}{5}$ .

Flashcard 39: For which values of $p$ does $\sum_{n=1}^{\infty} \frac{1}{n^p}$ diverge?

Answer: $p \leq 1$ . P-series diverge when $p$ is at most 1.

Flashcard 40: State the formula for a p-series.

Answer: $\sum_{n=1}^{\infty} \frac{1}{n^p}$ . General form where $p$ determines convergence behavior.

Flashcard 41: For which $p$ is the series $\sum_{n=1}^{\infty} \frac{1}{n^p}$ divergent?

Answer: $p \leq 1$ . P-series diverge when $p$ is at most 1.

Flashcard 42: State whether $\sum_{n=1}^{\infty} \frac{1}{n^{2.5}}$ converges.

Answer: Converges. Since $p = 2.5 > 1$ , this p-series converges.

Flashcard 43: Which series is divergent: $\sum_{n=1}^{\infty} \frac{1}{n}$ or $\sum_{n=1}^{\infty} \frac{1}{n^2}$ ?

Answer: $\sum_{n=1}^{\infty} \frac{1}{n}$ . The harmonic series diverges while $\sum \frac{1}{n^2}$ converges.

Flashcard 44: What condition makes a p-series diverge?

Answer: Diverges if $p \leq 1$ . When $p \leq 1$ , terms don't decrease fast enough.

Flashcard 45: Identify the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^2}$ .

Answer: Converges. Since $p = 2 > 1$ , this p-series converges.

Flashcard 46: Is $\sum_{n=1}^{\infty} \frac{1}{n^{0.5}}$ convergent or divergent?

Answer: Divergent. Since $p = 0.5 \leq 1$ , this p-series diverges.

Flashcard 47: What is the first term of a harmonic series?

Answer:

The harmonic series starts with $\frac{1}{1} = 1$ .

Flashcard 48: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{0.3}}$ ?

Answer: p-series. Has form $\sum \frac{1}{n^p}$ with $p = 0.3$ .

Flashcard 49: Determine the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{4}}$ .

Answer: Converges. Since $p = 4 > 1$ , this p-series converges.

Flashcard 50: What is the third term of a harmonic series?

Answer: $\frac{1}{3}$ . The third term in the harmonic series is $\frac{1}{3}$ .

Flashcard 51: Does the series $\sum_{n=1}^{\infty} \frac{1}{n^{3.5}}$ converge?

Answer: Converges. Since $p = 3.5 > 1$ , this p-series converges.

Flashcard 52: State the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{0.8}}$ .

Answer: Diverges. Since $p = 0.8 < 1$ , this p-series diverges.

Flashcard 53: What is the second term of a harmonic series?

Answer: $\frac{1}{2}$ . The second term in the harmonic series is $\frac{1}{2}$ .

Flashcard 54: State whether $\sum_{n=1}^{\infty} \frac{1}{n^{2.5}}$ converges.

Answer: Converges. Since $p = 2.5 > 1$ , this p-series converges.

Flashcard 55: What is the nature of $\sum_{n=1}^{\infty} \frac{1}{n^{2.1}}$ ?

Answer: Convergent. Since $p = 2.1 > 1$ , this p-series converges.

Flashcard 56: Identify if $\sum_{n=1}^{\infty} \frac{1}{n^{1/2}}$ converges or diverges.

Answer: Diverges. Since $p = 0.5 < 1$ , this p-series diverges.

Flashcard 57: What is the first term of a harmonic series?

Answer:

The harmonic series starts with $\frac{1}{1} = 1$ .

Flashcard 58: Does $\sum_{n=1}^{\infty} \frac{1}{n^{0.7}}$ converge or diverge?

Answer: Diverges. Since $p = 0.7 < 1$ , this p-series diverges.

Flashcard 59: What condition makes a p-series converge?

Answer: Converges if $p > 1$ . When $p > 1$ , the terms decrease fast enough for convergence.

AP Calculus BC Flashcards: Harmonic Series And P Series

Harmonic Series And P Series

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: What type of series is ∑n=1∞1n0.3\sum_{n=1}^{\infty} \frac{1}{n^{0.3}}∑n=1∞​n0.31​?

Flashcard 2: What is the condition for the convergence of a harmonic series?

Flashcard 3: Does the series ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞​n1​ converge or diverge?

Flashcard 4: Identify the convergence of ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞​n21​.

Flashcard 5: Is ∑n=1∞1n0.5\sum_{n=1}^{\infty} \frac{1}{n^{0.5}}∑n=1∞​n0.51​ convergent or divergent?

Flashcard 6: What type of series is ∑n=1∞1n1.5\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}∑n=1∞​n1.51​?

Flashcard 7: What is the nature of ∑n=1∞1n2.1\sum_{n=1}^{\infty} \frac{1}{n^{2.1}}∑n=1∞​n2.11​?

Flashcard 8: What is the fifth term of a harmonic series?

Flashcard 9: Does the series ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞​n1​ converge or diverge?

Flashcard 10: Identify the series that converges: ∑n=1∞1n3\sum_{n=1}^{\infty} \frac{1}{n^3}∑n=1∞​n31​ or ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞​n1​.

Flashcard 11: Identify if ∑n=1∞1n1/2\sum_{n=1}^{\infty} \frac{1}{n^{1/2}}∑n=1∞​n1/21​ converges or diverges.

Flashcard 12: For which values of ppp does ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞​np1​ diverge?

Flashcard 13: What is the condition for the convergence of a harmonic series?

Flashcard 14: What is the fourth term of a harmonic series?

Flashcard 15: Does the series ∑n=1∞1n3.5\sum_{n=1}^{\infty} \frac{1}{n^{3.5}}∑n=1∞​n3.51​ converge?

Flashcard 16: State the convergence of ∑n=1∞1n0.8\sum_{n=1}^{\infty} \frac{1}{n^{0.8}}∑n=1∞​n0.81​.

Flashcard 17: Identify if the series ∑n=1∞1n0.6\sum_{n=1}^{\infty} \frac{1}{n^{0.6}}∑n=1∞​n0.61​ is convergent.

Flashcard 18: What condition makes a p-series converge?

Flashcard 19: Identify the type of series: ∑n=1∞1n0.9\sum_{n=1}^{\infty} \frac{1}{n^{0.9}}∑n=1∞​n0.91​.

Flashcard 20: What is the second term of a harmonic series?

Flashcard 21: For which ppp is the series ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞​np1​ divergent?

Flashcard 22: Does ∑n=1∞1n0.7\sum_{n=1}^{\infty} \frac{1}{n^{0.7}}∑n=1∞​n0.71​ converge or diverge?

Flashcard 23: Determine the convergence of ∑n=1∞1n4\sum_{n=1}^{\infty} \frac{1}{n^{4}}∑n=1∞​n41​.

Flashcard 24: Identify if the series ∑n=1∞1n0.6\sum_{n=1}^{\infty} \frac{1}{n^{0.6}}∑n=1∞​n0.61​ is convergent.

Flashcard 25: Identify the series that converges: ∑n=1∞1n3\sum_{n=1}^{\infty} \frac{1}{n^3}∑n=1∞​n31​ or ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞​n1​.

Flashcard 26: Identify if the series ∑n=1∞1n1.5\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}∑n=1∞​n1.51​ converges.

Flashcard 27: Identify if ∑n=1∞1n3/2\sum_{n=1}^{\infty} \frac{1}{n^{3/2}}∑n=1∞​n3/21​ converges or diverges.

Flashcard 28: What is the definition of a harmonic series?

Flashcard 29: Identify if the series ∑n=1∞1n1.5\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}∑n=1∞​n1.51​ converges.

Flashcard 30: Which series is divergent: ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞​n1​ or ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞​n21​?

Flashcard 31: What is the third term of a harmonic series?

Flashcard 32: Identify the type of series: ∑n=1∞1n0.9\sum_{n=1}^{\infty} \frac{1}{n^{0.9}}∑n=1∞​n0.91​.

Flashcard 33: What type of series is ∑n=1∞1n1.5\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}∑n=1∞​n1.51​?

Flashcard 34: What condition makes a p-series diverge?

Flashcard 35: What is the fourth term of a harmonic series?

Flashcard 36: State the formula for a p-series.

Flashcard 37: What is the definition of a harmonic series?

Flashcard 38: What is the fifth term of a harmonic series?

Flashcard 39: For which values of ppp does ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞​np1​ diverge?

Flashcard 40: State the formula for a p-series.

Flashcard 41: For which ppp is the series ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞​np1​ divergent?

Flashcard 42: State whether ∑n=1∞1n2.5\sum_{n=1}^{\infty} \frac{1}{n^{2.5}}∑n=1∞​n2.51​ converges.

Flashcard 43: Which series is divergent: ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞​n1​ or ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞​n21​?

Flashcard 44: What condition makes a p-series diverge?

Flashcard 45: Identify the convergence of ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞​n21​.

Flashcard 46: Is ∑n=1∞1n0.5\sum_{n=1}^{\infty} \frac{1}{n^{0.5}}∑n=1∞​n0.51​ convergent or divergent?

Flashcard 47: What is the first term of a harmonic series?

Flashcard 48: What type of series is ∑n=1∞1n0.3\sum_{n=1}^{\infty} \frac{1}{n^{0.3}}∑n=1∞​n0.31​?

Flashcard 49: Determine the convergence of ∑n=1∞1n4\sum_{n=1}^{\infty} \frac{1}{n^{4}}∑n=1∞​n41​.

Flashcard 50: What is the third term of a harmonic series?

Flashcard 51: Does the series ∑n=1∞1n3.5\sum_{n=1}^{\infty} \frac{1}{n^{3.5}}∑n=1∞​n3.51​ converge?

Flashcard 52: State the convergence of ∑n=1∞1n0.8\sum_{n=1}^{\infty} \frac{1}{n^{0.8}}∑n=1∞​n0.81​.

Flashcard 53: What is the second term of a harmonic series?

Flashcard 54: State whether ∑n=1∞1n2.5\sum_{n=1}^{\infty} \frac{1}{n^{2.5}}∑n=1∞​n2.51​ converges.

Flashcard 55: What is the nature of ∑n=1∞1n2.1\sum_{n=1}^{\infty} \frac{1}{n^{2.1}}∑n=1∞​n2.11​?

Flashcard 56: Identify if ∑n=1∞1n1/2\sum_{n=1}^{\infty} \frac{1}{n^{1/2}}∑n=1∞​n1/21​ converges or diverges.

Flashcard 57: What is the first term of a harmonic series?

Flashcard 58: Does ∑n=1∞1n0.7\sum_{n=1}^{\infty} \frac{1}{n^{0.7}}∑n=1∞​n0.71​ converge or diverge?

Flashcard 59: What condition makes a p-series converge?

Flashcard 1: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{0.3}}$ ?

Flashcard 3: Does the series $\sum_{n=1}^{\infty} \frac{1}{n}$ converge or diverge?

Flashcard 4: Identify the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^2}$ .

Flashcard 5: Is $\sum_{n=1}^{\infty} \frac{1}{n^{0.5}}$ convergent or divergent?

Flashcard 6: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ ?

Flashcard 7: What is the nature of $\sum_{n=1}^{\infty} \frac{1}{n^{2.1}}$ ?

Flashcard 9: Does the series $\sum_{n=1}^{\infty} \frac{1}{n}$ converge or diverge?

Flashcard 10: Identify the series that converges: $\sum_{n=1}^{\infty} \frac{1}{n^3}$ or $\sum_{n=1}^{\infty} \frac{1}{n}$ .

Flashcard 11: Identify if $\sum_{n=1}^{\infty} \frac{1}{n^{1/2}}$ converges or diverges.

Flashcard 12: For which values of $p$ does $\sum_{n=1}^{\infty} \frac{1}{n^p}$ diverge?

Flashcard 15: Does the series $\sum_{n=1}^{\infty} \frac{1}{n^{3.5}}$ converge?

Flashcard 16: State the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{0.8}}$ .

Flashcard 17: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{0.6}}$ is convergent.

Flashcard 19: Identify the type of series: $\sum_{n=1}^{\infty} \frac{1}{n^{0.9}}$ .

Flashcard 21: For which $p$ is the series $\sum_{n=1}^{\infty} \frac{1}{n^p}$ divergent?

Flashcard 22: Does $\sum_{n=1}^{\infty} \frac{1}{n^{0.7}}$ converge or diverge?

Flashcard 23: Determine the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{4}}$ .

Flashcard 24: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{0.6}}$ is convergent.

Flashcard 25: Identify the series that converges: $\sum_{n=1}^{\infty} \frac{1}{n^3}$ or $\sum_{n=1}^{\infty} \frac{1}{n}$ .

Flashcard 26: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ converges.

Flashcard 27: Identify if $\sum_{n=1}^{\infty} \frac{1}{n^{3/2}}$ converges or diverges.

Flashcard 29: Identify if the series $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ converges.

Flashcard 30: Which series is divergent: $\sum_{n=1}^{\infty} \frac{1}{n}$ or $\sum_{n=1}^{\infty} \frac{1}{n^2}$ ?

Flashcard 32: Identify the type of series: $\sum_{n=1}^{\infty} \frac{1}{n^{0.9}}$ .

Flashcard 33: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}$ ?

Flashcard 39: For which values of $p$ does $\sum_{n=1}^{\infty} \frac{1}{n^p}$ diverge?

Flashcard 41: For which $p$ is the series $\sum_{n=1}^{\infty} \frac{1}{n^p}$ divergent?

Flashcard 42: State whether $\sum_{n=1}^{\infty} \frac{1}{n^{2.5}}$ converges.

Flashcard 43: Which series is divergent: $\sum_{n=1}^{\infty} \frac{1}{n}$ or $\sum_{n=1}^{\infty} \frac{1}{n^2}$ ?

Flashcard 45: Identify the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^2}$ .

Flashcard 46: Is $\sum_{n=1}^{\infty} \frac{1}{n^{0.5}}$ convergent or divergent?

Flashcard 48: What type of series is $\sum_{n=1}^{\infty} \frac{1}{n^{0.3}}$ ?

Flashcard 49: Determine the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{4}}$ .

Flashcard 51: Does the series $\sum_{n=1}^{\infty} \frac{1}{n^{3.5}}$ converge?

Flashcard 52: State the convergence of $\sum_{n=1}^{\infty} \frac{1}{n^{0.8}}$ .

Flashcard 54: State whether $\sum_{n=1}^{\infty} \frac{1}{n^{2.5}}$ converges.

Flashcard 55: What is the nature of $\sum_{n=1}^{\infty} \frac{1}{n^{2.1}}$ ?

Flashcard 56: Identify if $\sum_{n=1}^{\infty} \frac{1}{n^{1/2}}$ converges or diverges.

Flashcard 58: Does $\sum_{n=1}^{\infty} \frac{1}{n^{0.7}}$ converge or diverge?