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

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

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

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

diverges

Solution steps

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

Simplify

2^{n} \cdot \frac{1}{n ^{2}} : \frac{2 ^{n}}{n ^{2}}

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

Apply Series Ratio Test:

diverges

= diverges

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