Find a Formula for the Nth Partial Sum of the Series

question 70

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

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