Find the values of x for which the geometric series converges.
-$$\sum _ { n = 0 } ^ { \infty } ( x + 4 ) ^ { n }$$
A) -5

Question

Find the values of x for which the geometric series converges.
-$$\sum _ { n = 0 } ^ { \infty } ( x + 4 ) ^ { n }$$
A) -5 < x < -4
B) -5 < x < -3
C) -4 < x < 4
D) -4 < x < -3

Quizplus · Accepted Answer

A geometric series converges if the absolute value of the common ratio is less than 1. Here, the common ratio is $x + 4$. Therefore, $|x + 4| < 1$, which simplifies to $-1 < x + 4 < 1$. Solving this inequality gives $-5 < x < -3$.

Find the Values of X for Which the Geometric Series ∑n=0∞(x+4)n\sum _ { n = 0 } ^ { \infty } ( x + 4 ) ^ { n }n=0∑∞​(x+4)n

Find the Values of X for Which the Geometric Series $\sum _ { n = 0 } ^ { \infty } ( x + 4 ) ^ { n }$