What is the sum from n=1 to infinity of n/(6n^3+5) ?

The sum from n=1 to infinity of n/(6n^3+5) is converges

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sum from n=1 to infinity of n/(6n^3+5)

n = 1 \sum \infty \frac{n}{6 n ^{3} + 5}

converges

Solution steps

n = 1 \sum \infty \frac{n}{6 n ^{3} + 5}

Apply Series Comparison Test:

converges

= converges

n = 0 \sum \infty 5 n^{2}

n = 2 \sum \infty \frac{1}{3 n + 4}

n = 1 \sum \infty 3 (0.4)^{n - 1}

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

n = 0 \sum \infty - (\frac{7}{3 ^{n}})

What is the sum from n=1 to infinity of n/(6n^3+5) ?
The sum from n=1 to infinity of n/(6n^3+5) is converges