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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{2}{5 ^{n} - 4}

n = 0 \sum \infty \frac{n}{7 n + 1}

n = 1 \sum \infty \frac{n}{n ^{2} + 2 n + 3}

n = 1 \sum \infty (n!) e^{- n}

n = 1 \sum \infty \frac{e ^{\frac{3}{n}}}{n}

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