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

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

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

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

diverges

Solution steps

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

Simplify

\frac{n ^{2}}{n ^{3}} : \frac{1}{n}

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

Apply Cauchy's Convergence Condition:

diverges

= diverges

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