Use Summation Notation to Write the Given Series in Compact $$\frac { 1 } { 4 } - \frac { 2 } { 16 } + \frac { 3 } { 64 } - \frac { 4 } { 256 } + \cdots$$

Use summation notation to write the given series in compact form. $$\frac { 1 } { 4 } - \frac { 2 } { 16 } + \frac { 3 } { 64 } - \frac { 4 } { 256 } + \cdots$$

A) $\sum _ { n = 1 } ^ { \infty } n ( - 1 ) ^ { n - 1 } \left( \frac { 1 } { 4 } \right) ^ { n }$
B) $\sum _ { n = 1 } ^ { \infty } \frac { - n } { 4 ^ { n } }$
C) $\sum _ { n = 1 } ^ { \infty } \frac { n } { 4 ^ { n } }$
D) $\sum _ { n = 1 } ^ { \infty } \left( - \frac { n } { 4 } \right) ^ { n }$

Correct Answer:

Verified

Show Answer