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Question
\sum _{n=0}^{+\infty}\frac{n!}{5^{n}}
Determine the convergence or divergence
\textrm{Diverges}
Evaluate
\sum _{n=0}^{+\infty}\frac{n!}{5^{n}}
Find the limit
\lim _{n\rightarrow +\infty}\left(\left|\frac{\frac{\left(n+1\right)!}{5^{n+1}}}{\frac{n!}{5^{n}}}\right|\right)
Simplify
\lim _{n\rightarrow +\infty}\left(\left|\frac{n+1}{5}\right|\right)
Remove the absolute value bars
\lim _{n\rightarrow +\infty}\left(\frac{n+1}{5}\right)
Rewrite the expression
\frac{\lim _{n\rightarrow +\infty}\left(n+1\right)}{5}
Calculate
More Steps
Evaluate
\lim _{n\rightarrow +\infty}\left(n+1\right)
Rewrite the expression
\lim _{n\rightarrow +\infty}\left(n\right)+\lim _{n\rightarrow +\infty}\left(1\right)
Calculate
\left(+\infty\right)+\lim _{n\rightarrow +\infty}\left(1\right)
Calculate
\left(+\infty\right)+1
Calculate
+\infty
\frac{+\infty}{5}
Calculate
+\infty
Solution
\textrm{Diverges}
Show Solutions
