Find the sum of the geometric series for those x for which the series converges.
-$$\sum _ { n = 0 } ^ { \infty } 7 ^ { n } x ^ { n }$$
A) $\frac { 1 } { 1 + 7 x }$
B) $\frac { 1 } { 1 - 7 x }$
C) $\frac { 7 } { 1 + 7 x }$
D) $\frac { 7 } { 1 - 7 x }$

Question

Quizplus · Accepted Answer

The given series is a geometric series with first term 1 and common ratio 7x. Therefore, it will converge if and only if $|7x|<1$, or equivalently, $-1/7<x<1/7$. Using the formula for the sum of a geometric series, we have
$$\sum _ { n = 0 } ^ { \infty } 7 ^ { n } x ^ { n } = \frac{1}{1-7x}$$ only if $-1/7<x<1/7$, and diverges otherwise. Therefore, choice B is the correct answer.

Find the Sum of the Geometric Series for Those X ∑n=0∞7nxn\sum _ { n = 0 } ^ { \infty } 7 ^ { n } x ^ { n }n=0∑∞​7nxn

Find the Sum of the Geometric Series for Those X $\sum _ { n = 0 } ^ { \infty } 7 ^ { n } x ^ { n }$