What is the sum from n=0 to infinity of (2^n)/(n^2) ?

The sum from n=0 to infinity of (2^n)/(n^2) is diverges

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sum from n=0 to infinity of (2^n)/(n^2)

n = 0 \sum \infty \frac{2 ^{n}}{n ^{2}}

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

f (x) = \frac{2}{3} x - 6

\int \frac{6}{x ^{2} x ^{2} + 36} d x

\int_{1}^{8} 3 x^{2} + \frac{1}{12 x ^{2}} d x

\int \frac{x ^{2}}{( x - 1 ) ^{4}} d x

\frac{x ^{3} - 4}{x ^{2} + 2}

What is the sum from n=0 to infinity of (2^n)/(n^2) ?
The sum from n=0 to infinity of (2^n)/(n^2) is diverges