Find the values of x for which the geometric series converges.
-$$\sum _ { n = 0 } ^ { \infty } 10 ^ { n } x ^ { n }$$
A) $| x |

Question

Find the values of x for which the geometric series converges.
-$$\sum _ { n = 0 } ^ { \infty } 10 ^ { n } x ^ { n }$$
A) $| x | < \frac { 1 } { 10 }$
B) $| x | < 1$
C) $| x | < 10$
D) $| x | < 20$

Quizplus · Accepted Answer

A geometric series converges if and only if the absolute value of the common ratio is less than 1. Here, the common ratio is $10x$, so the series converges for $|10x| < 1$, which simplifies to $|x| < \frac{1}{10}$.

Find the Values of X for Which the Geometric Series ∑n=0∞10nxn\sum _ { n = 0 } ^ { \infty } 10 ^ { n } x ^ { n }n=0∑∞​10nxn

Find the Values of X for Which the Geometric Series $\sum _ { n = 0 } ^ { \infty } 10 ^ { n } x ^ { n }$