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

This is a geometric series with first term $5$ and common ratio $\frac{6^{-1}}{5} = \frac{6^{-1}}{5^{-1}}$, so the series converges and its sum is 
$$\frac{5}{1-\frac{6^{-1}}{5}} = \frac{5}{\frac{4}{5}} = \boxed{36}.$$

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 $\sum _ { n = 0 } ^ { \infty } 5 ^ { n } 6 ^ { - n + 1 }$