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

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

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

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

diverges

Solution steps

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

Apply Series Integral Test:

diverges

= diverges

\int (\frac{x ^{2}}{2} - \frac{2}{x ^{2}}) d x

\frac{\partial}{\partial x} (\frac{3 y}{x ^{2} + 2})

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}})

x - x^{3}

\frac{d}{d x} (\frac{x}{( 1 + x )})

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