What is the sum from n=1 to infinity of 1/(5^n+n) ?

The sum from n=1 to infinity of 1/(5^n+n) is converges

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sum from n=1 to infinity of 1/(5^n+n)

n = 1 \sum \infty \frac{1}{5 ^{n} + n}

converges

Solution steps

n = 1 \sum \infty \frac{1}{5 ^{n} + n}

Apply Series Ratio Test:

converges

= converges

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

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

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

n = 1 \sum \infty \frac{n}{9 ^{n}}

What is the sum from n=1 to infinity of 1/(5^n+n) ?
The sum from n=1 to infinity of 1/(5^n+n) is converges