What is the sum from n=0 to infinity of n/(4+n^2) ?

The sum from n=0 to infinity of n/(4+n^2) is diverges

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sum from n=0 to infinity of n/(4+n^2)

n = 0 \sum \infty \frac{n}{4 + n ^{2}}

diverges

Solution steps

n = 0 \sum \infty \frac{n}{4 + n ^{2}}

Apply Series Integral Test:

diverges

= diverges

n = 0 \sum \infty \frac{1}{n}

n = 1 \sum \infty ln (\frac{1}{n !})

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

n = 1 \sum \infty \frac{9 ^{n}}{n ^{5}}

n = 1 \sum \infty \frac{1}{9 n ^{3}}

What is the sum from n=0 to infinity of n/(4+n^2) ?
The sum from n=0 to infinity of n/(4+n^2) is diverges