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

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

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

n = 0 \sum \infty \frac{n}{n ^{3}}

converges

Solution steps

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

Cancel the common factor:

n

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

Apply p-Series Test:

converges

= converges

n = 6 \sum \infty ln (\frac{n}{3})

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

n = 1 \sum \infty 2 (\frac{1}{4})^{n - 1}

n = 1 \sum \infty \frac{4}{n ^{- 2.3}}

n = 0 \sum \infty (- 0.2)^{n}

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