What is the sum from n=0 to infinity of n/(2n^3+1) ?

The sum from n=0 to infinity of n/(2n^3+1) is converges

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sum from n=0 to infinity of n/(2n^3+1)

n = 0 \sum \infty \frac{n}{2 n ^{3} + 1}

converges

Solution steps

n = 0 \sum \infty \frac{n}{2 n ^{3} + 1}

Apply Series Comparison Test:

converges

= converges

n = 0 \sum \infty n

n = 1 \sum \infty (\frac{5 π}{6})^{n}

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

n = 0 \sum \infty \frac{1}{6 - n}

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

What is the sum from n=0 to infinity of n/(2n^3+1) ?
The sum from n=0 to infinity of n/(2n^3+1) is converges