What is the sum from n=0 to infinity of 1/(2^n+n^2) ?

The sum from n=0 to infinity of 1/(2^n+n^2) is converges

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sum from n=0 to infinity of 1/(2^n+n^2)

n = 0 \sum \infty \frac{1}{2 ^{n} + n ^{2}}

converges

Solution steps

n = 0 \sum \infty \frac{1}{2 ^{n} + n ^{2}}

Apply Series Ratio Test:

converges

= converges

k = 2 \sum \infty \frac{1}{ln ( k )}

n = 1 \sum \infty \frac{1}{n ^{2} + 16}

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

n = 0 \sum \infty (\frac{5}{8})^{n}

n = 0 \sum \infty \frac{e ^{n}}{n ^{3}}

What is the sum from n=0 to infinity of 1/(2^n+n^2) ?
The sum from n=0 to infinity of 1/(2^n+n^2) is converges