Determine if the series converges or diverges; if the series converges, find its sum.
-$$\sum _ { n = 0 } ^ { \infty } \frac { n ! } { 900 ^ { n } }$$
A) Converges; $\mathrm { e }$
B) Converges; 1
C) converges; $\frac { 1 } { \mathrm { e } }$
D) Diverges

Question

Quizplus · Accepted Answer

The series diverges because the ratio of successive terms does not approach zero as $n$ approaches infinity. The factorial $n!$ grows much faster than $900^n$, leading to divergence.

Determine If the Series Converges or Diverges; If the Series ∑n=0∞n!900n\sum _ { n = 0 } ^ { \infty } \frac { n ! } { 900 ^ { n } }n=0∑∞​900nn!​

Determine If the Series Converges or Diverges; If the Series $\sum _ { n = 0 } ^ { \infty } \frac { n ! } { 900 ^ { n } }$