?

AP® Calculus AB-BC

Free Version

Upgrade subject to access all content

Difficult

Limit of a Series Using Partial Sums

APCALC-UBGK9L

Determine the nth 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