What is the sum from n=1 to infinity of (4^n)/(n^2) ?

The sum from n=1 to infinity of (4^n)/(n^2) is diverges

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sum from n=1 to infinity of (4^n)/(n^2)

n = 1 \sum \infty \frac{4 ^{n}}{n ^{2}}

diverges

Solution steps

n = 1 \sum \infty \frac{4 ^{n}}{n ^{2}}

n \to \infty lim (n (\frac{\frac{4 ^{n}}{n ^{2}}}{\frac{4 ^{n + 1}}{( n + 1 ) ^{2}}} - 1)) = - \infty

L < 1,

by the Raabe's test

= diverges

\frac{1}{1 + x ^{2}}

f (x) = \frac{x + 2}{x - 2}

\int ln ((3 x)^{2}) d x

f (x) = (x + 3) (5 x^{2} - 7 x)

\int \frac{- 8 x ^{2} + 16 x + 8}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

What is the sum from n=1 to infinity of (4^n)/(n^2) ?
The sum from n=1 to infinity of (4^n)/(n^2) is diverges