Find a Formula for the Nth Partial Sum of the Series

question 308

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.
- $$\frac { 7 } { 1 \cdot 2 } + \frac { 7 } { 2 \cdot 3 } + \frac { 7 } { 3 \cdot 4 } + \ldots + \frac { 7 } { \mathrm { n } ( \mathrm { n } + 1 ) } + \ldots$$

• A) \(\frac { 7 ( \mathrm { n } + 1 ) } { \mathrm { n } } ; 7\)
• B) \(\frac { 7 ( n + 2 ) } { n + 1 } ; 7\)
• C) \(\frac { 7 ( n + 1 ) } { n + 2 } ; 7\)
• D) \(\frac { 7 \mathrm { n } } { \mathrm { n } + 1 } ; 7\)