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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

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

n = 0 \sum \infty \frac{- 1 ^{n}}{n}

n = 1 \sum \infty \frac{6}{n ^{\frac{4}{3}}}

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

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