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

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

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

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

diverges

Solution steps

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

Simplify

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

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

Apply Series Limit Comparison Test:

diverges

= diverges

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