Find a Formula for the Nth Partial Sum of the Series

question 31

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.
- $$7 + \frac { 7 } { 4 } + \frac { 7 } { 16 } + \ldots + \frac { 7 } { 4 ^ { n - 1 } } + \ldots$$

• A) \(\frac { \left( 1 - \frac { 1 } { 4 ^ { n } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 5 }\)
• B) \(\frac { 7 \left( 1 - \frac { 1 } { 4 ^ { n - 1 } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 5 }\)
• C) \(\frac { 7 \left( 1 - \frac { 1 } { 4 ^ { n - 1 } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 3 }\)
• D) \(\frac { 7 \left( 1 - \frac { 1 } { 4 ^ { n } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 3 }\)