AP® Calculus AB-BC

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Limit of a Series Using Partial Sums

APCALC-UBGK9L

Determine the $n^{th}$ partial sum of the series $\sum_{n=1}^{\infty }\frac{1}{n\left ( n+1 \right )}$ and identify the series as convergent or divergent.

A

$S_{n}=\cfrac{1}{n^{2}+n}$, convergent.

B

$S_{n}=\cfrac{1}{n^{2}+n}$, divergent.

C

$S_{n}=\cfrac{n}{n+1}$, convergent.

D

$S_{n}=\cfrac{n}{n+1}$, divergent.