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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

\frac{d}{d x} (\frac{x}{2})

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 0

x \to - 1 + lim (\frac{3 x - 5}{x + 1})

- \frac{3}{x}

(arctan (cos (x)))^{^{'}}

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