Find the sum of the geometric series for those x for which the series converges.
-$$\sum _ { n = 0 } ^ { \infty } ( x - 5 ) ^ { n }$$
A) $\frac { 1 } { - 4 - x }$
B) $\frac { 1 } { - 4 + x }$
C) $\frac { 1 } { 6 + x }$
D) $\frac { 1 } { 6 - x }$

Question

Quizplus · Accepted Answer

The series converges when the absolute value of the common ratio $|x - 5| < 1$, which simplifies to $4 < x < 6$. The sum of the series is $\frac{1}{1 - (x - 5)} = \frac{1}{6 - x}$.

Find the Sum of the Geometric Series for Those X ∑n=0∞(x−5)n\sum _ { n = 0 } ^ { \infty } ( x - 5 ) ^ { n }n=0∑∞​(x−5)n

Find the Sum of the Geometric Series for Those X $\sum _ { n = 0 } ^ { \infty } ( x - 5 ) ^ { n }$