Determine whether the geometric series converges or diverges.If it converges, find its sum. $$\sum _ { n = 0 } ^ { \infty } 5 ^ { n } 6 ^ { - n + 1 }$$
A) 30
B) 36
C) 5
D) Diverges

Question

Quizplus · Accepted Answer

The series can be written as $\sum_{n=0}^{\infty}\left(\frac{5}{6}ight)^n6$. This is a geometric series with first term $6$ and ratio $\frac{5}{6}$, which converges since $|\frac{5}{6}|<1$. Thus, by the formula for the sum of an infinite geometric series, the sum is $\frac{6}{1-\frac{5}{6}}=\boxed{	extbf{(B)}\ 36}$.

Determine Whether the Geometric Series Converges or Diverges ∑n=0∞5n6−n+1\sum _ { n = 0 } ^ { \infty } 5 ^ { n } 6 ^ { - n + 1 }n=0∑∞​5n6−n+1

Determine Whether the Geometric Series Converges or Diverges $\sum _ { n = 0 } ^ { \infty } 5 ^ { n } 6 ^ { - n + 1 }$