The nth Term Test for Divergence
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Identify
lim
n
→
∞
4
n
3
2
n
3
\lim_{{n \to \infty}} \frac{4n^3}{2n^3}
lim
n
→
∞
2
n
3
4
n
3
. Divergent?
QUESTION
Evaluate
lim
n
→
∞
2
n
\lim_{{n \to \infty}} \frac{2}{n}
lim
n
→
∞
n
2
. Divergent?
QUESTION
Evaluate
lim
n
→
∞
n
3
n
2
+
1
\lim_{{n \to \infty}} \frac{n^3}{n^2 + 1}
lim
n
→
∞
n
2
+
1
n
3
. Divergent?
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ANSWER
Limit is
∞
\infty
∞
; series diverges. Degree of numerator exceeds denominator, so limit is infinite.
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