What is the sum from n=1 to infinity of 1/(n^3+5) ?

The sum from n=1 to infinity of 1/(n^3+5) is converges

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sum from n=1 to infinity of 1/(n^3+5)

n = 1 \sum \infty \frac{1}{n ^{3} + 5}

converges

Solution steps

n = 1 \sum \infty \frac{1}{n ^{3} + 5}

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty \frac{1}{n ^{3} - 5 n ^{2}}

k = 1 \sum \infty \frac{k ^{2}}{4 ^{k}}

n = 0 \sum \infty n 2^{n}

n = 1 \sum \infty \frac{1}{( 2 ^{n} )}

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

What is the sum from n=1 to infinity of 1/(n^3+5) ?
The sum from n=1 to infinity of 1/(n^3+5) is converges