Harmonic Series and p-Series
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Does the series
∑
n
=
1
∞
1
n
\sum_{n=1}^{\infty} \frac{1}{n}
∑
n
=
1
∞
n
1
converge or diverge?
QUESTION
What is the nature of
∑
n
=
1
∞
1
n
2.1
\sum_{n=1}^{\infty} \frac{1}{n^{2.1}}
∑
n
=
1
∞
n
2.1
1
?
QUESTION
Identify the convergence of
∑
n
=
1
∞
1
n
2
\sum_{n=1}^{\infty} \frac{1}{n^2}
∑
n
=
1
∞
n
2
1
.
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ANSWER
Converges. Since
p
=
2
>
1
p = 2 > 1
p
=
2
>
1
, this p-series converges.
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