Find All Values of X for Which the Series Converges $$\sum _ { n = 0 } ^ { \infty } 10 \left( \frac { x - 8 } { 10 } \right) ^ { n }$$

Multiple Choice

Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x. $$\sum _ { n = 0 } ^ { \infty } 10 \left( \frac { x - 8 } { 10 } \right) ^ { n }$$

A) $- \frac { 100 } { 18 - x } , - 2 < x < 18$
B) $\frac { 100 } { 18 - x } , - 2 < x < 18$
C) $\frac { 100 } { 28 + x } , - 12 < x < 28$
D) $\frac { 100 } { 28 - x } , - 12 < x < 28$
E) The series diverges for all $x$ .