What is the sum from n=1 to infinity of (5^n)/(n^2) ?

The sum from n=1 to infinity of (5^n)/(n^2) is diverges

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sum from n=1 to infinity of (5^n)/(n^2)

n = 1 \sum \infty \frac{5 ^{n}}{n ^{2}}

diverges

Solution steps

n = 1 \sum \infty \frac{5 ^{n}}{n ^{2}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{n ^{2}}}{\frac{5 ^{n + 1}}{( n + 1 ) ^{2}}} - 1)) = - \infty

L < 1,

by the Raabe's test

= diverges

n = 4 \sum \infty \frac{3}{n ^{2} - n}

k = 1 \sum \infty \frac{6 k ^{5}}{k !}

m = 2 \sum \infty \frac{2}{3 ^{m}}

n = 4 \sum \infty \frac{1}{n ( n - 1 )}

n = 0 \sum \infty \frac{1}{( 1 - 3 n ) ^{3}}

What is the sum from n=1 to infinity of (5^n)/(n^2) ?
The sum from n=1 to infinity of (5^n)/(n^2) is diverges