Find the values of $x$ for which the series
$\sum _ { n = 0 } ^ { \infty } 9 ( x - 1 ) ^ { n }$ converges.
A) $8

Question

Find the values of $x$ for which the series
$\sum _ { n = 0 } ^ { \infty } 9 ( x - 1 ) ^ { n }$ converges. 
A) $8 < x < 10$
B) $- 1 < x < 1$
C) $- 9 < x < 0$
D) $0 < x < 2$
E) $- 2 < x < 0$

Quizplus · Accepted Answer

The series given is a geometric series with the common ratio $r = x - 1$. For a geometric series to converge, the absolute value of the common ratio must be less than 1, i.e., $|x - 1| < 1$. Solving this inequality gives $0 < x < 2$.

Find the Values Of xxx For Which the Series ∑n=0∞9(x−1)n\sum _ { n = 0 } ^ { \infty } 9 ( x - 1 ) ^ { n }∑n=0∞​9(x−1)n

Find the Values Of $x$ For Which the Series $\sum _ { n = 0 } ^ { \infty } 9 ( x - 1 ) ^ { n }$