Find a Formula for the Nth Partial Sum of the Series

question 97

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.
- $\frac { 2 } { 1 \cdot 2 } + \frac { 2 } { 2 \cdot 3 } + \frac { 2 } { 3 \cdot 4 } + \ldots + \frac { 2 } { n ( n + 1 ) } + \ldots$

• A) \(\frac { 2 ( n + 2 ) } { n + 1 } ; 2\)
• B) \(\frac { 2 ( n + 1 ) } { n } ; 2\)
• C) \(\frac { 2 ( n + 1 ) } { n + 2 } ; 2\)
• D) \(\frac { 2 n } { n + 1 } ; 2\)

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