Find a Formula for the Nth Partial Sum of the Series

question 99

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.
- $7 + 14 + 28 + \ldots + 7 \cdot 2 ^ { n - 1 } + \ldots$

• A) \(\frac { 7 \left( 1 + 2 ^ { n } \right) } { 1 + 2 } ; \frac { 7 } { 3 }\)
• B) \(\frac { 7 \left( 1 - 2 ^ { n } \right) } { 1 - 2 } ; 7\)
• C) \(\frac { 7 \left( 1 - 2 ^ { n } \right) } { 2 - 1 } ;\) series diverges
• D) \(\frac { 7 \left( 1 - 2 ^ { n } \right) } { 1 - 2 }\); series diverges

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