Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
-$$\frac { 4 } { 2 \cdot 3 } + \frac { 4 } { 3 \cdot 4 } + \frac { 4 } { 4 \cdot 5 } + \ldots + \frac { 4 } { ( n + 1 ) ( n + 2 ) } + \ldots$$
A) $\frac { 4 \mathrm { n } } { \mathrm { n } + 2 } ; 4$
B) $\frac { 4 \mathrm { n } } { 2 ( \mathrm { n } + 2 ) } ; 2$
C) $\frac { 4 n } { 2 ( n + 1 ) } ; 2$
D) $\frac { 4 n } { n + 1 } ; 4$

Question

Quizplus · Accepted Answer

The series is telescoping. The nth partial sum is $\frac{4n}{2(n+2)}$, and as $n$ approaches infinity, the sum converges to 2.

Find a Formula for the Nth Partial Sum of the Series