Find a Formula for the Nth Partial Sum of the Series

Multiple Choice

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
- $$\frac { 2 } { 3 \cdot 1 } + \frac { 2 } { 5 \cdot 3 } + \frac { 2 } { 7 \cdot 5 } + \ldots + \frac { 2 } { ( 2 n + 1 ) ( 2 n - 1 ) } + \ldots$$

A) $\frac { 2 n } { 2 ( n + 1 ) } ; 1$

B) $\frac { 2 n } { n + 2 } ; 2$

C) $\frac { 4 n } { 2 n + 1 } ; 2$

D) $\frac { 2 n } { 2 n + 1 } ; 1$