Find the values of x for which the geometric series converges.
-$$\sum _ { n = 0 } ^ { \infty } - 6 ^ { n } x ^ { n }$$
A) $| x |

Name: Find the values of x for which the geometric series converges. -\[\sum _ { n = 0 } ^ { \infty } - 6 ^ { n } x ^ { n }\] A) $| x | < 6$ B) $| x | < \frac { 1 } { 6 }$ C) $| x | < 12$ D) $| x | < 1$
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Question

Find the values of x for which the geometric series converges.
-$$\sum _ { n = 0 } ^ { \infty } - 6 ^ { n } x ^ { n }$$
A) $| x | < 6$
B) $| x | < \frac { 1 } { 6 }$
C) $| x | < 12$
D) $| x | < 1$

Quizplus · Accepted Answer

For a geometric series $\sum a r^n$ to converge, the common ratio $|r| < 1$. Here, $r = -6x$, so $|-6x| < 1$, which simplifies to $|x| < \frac{1}{6}$.

Find the Values of X for Which the Geometric Series ∑n=0∞−6nxn\sum _ { n = 0 } ^ { \infty } - 6 ^ { n } x ^ { n }n=0∑∞​−6nxn

Find the Values of X for Which the Geometric Series $\sum _ { n = 0 } ^ { \infty } - 6 ^ { n } x ^ { n }$