What is the sum from n=1 to infinity of (5^n)/(n^4) ?

The sum from n=1 to infinity of (5^n)/(n^4) is diverges

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sum from n=1 to infinity of (5^n)/(n^4)

n = 1 \sum \infty \frac{5 ^{n}}{n ^{4}}

diverges

Solution steps

n = 1 \sum \infty \frac{5 ^{n}}{n ^{4}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{n ^{4}}}{\frac{5 ^{n + 1}}{( n + 1 ) ^{4}}} - 1)) = - \infty

L < 1,

by the Raabe's test

= diverges

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What is the sum from n=1 to infinity of (5^n)/(n^4) ?
The sum from n=1 to infinity of (5^n)/(n^4) is diverges