What is the sum from n=1 to infinity of 1/(2n^3+8) ?

The sum from n=1 to infinity of 1/(2n^3+8) is converges

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sum from n=1 to infinity of 1/(2n^3+8)

n = 1 \sum \infty \frac{1}{2 n ^{3} + 8}

converges

Solution steps

n = 1 \sum \infty \frac{1}{2 n ^{3} + 8}

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty \frac{5}{2 n}

n = 2 \sum \infty \frac{2}{n}

n = 0 \sum \infty (\frac{1}{14})^{n}

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

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

What is the sum from n=1 to infinity of 1/(2n^3+8) ?
The sum from n=1 to infinity of 1/(2n^3+8) is converges