What is the sum from n=0 to infinity of n/(n^2+7) ?

The sum from n=0 to infinity of n/(n^2+7) is diverges

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sum from n=0 to infinity of n/(n^2+7)

n = 0 \sum \infty \frac{n}{n ^{2} + 7}

diverges

Solution steps

n = 0 \sum \infty \frac{n}{n ^{2} + 7}

Apply Series Integral Test:

diverges

= diverges

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

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

n = 1 \sum \infty \frac{10}{2 ^{n}}

n = 0 \sum \infty \frac{7}{4 - n ^{2}}

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

What is the sum from n=0 to infinity of n/(n^2+7) ?
The sum from n=0 to infinity of n/(n^2+7) is diverges