What is the sum from n=0 to infinity of 1/(n^5+1) ?

The sum from n=0 to infinity of 1/(n^5+1) is converges

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sum from n=0 to infinity of 1/(n^5+1)

n = 0 \sum \infty \frac{1}{n ^{5} + 1}

converges

Solution steps

n = 0 \sum \infty \frac{1}{n ^{5} + 1}

Apply Series Comparison Test:

converges

= converges

k = 1 \sum \infty \frac{1}{k ^{5}}

n = 1 \sum \infty \frac{5}{5 n - 1}

n = 0 \sum \infty \frac{6}{n}

n = 1 \sum \infty n (\frac{5}{6})^{n}

n = 7 \sum \infty \frac{1}{n ^{2} - 5 n + 6}

What is the sum from n=0 to infinity of 1/(n^5+1) ?
The sum from n=0 to infinity of 1/(n^5+1) is converges