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

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

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

n = 2 \sum \infty \frac{n}{n ^{2} - 2}

diverges

Solution steps

n = 2 \sum \infty \frac{n}{n ^{2} - 2}

Apply Series Comparison Test:

diverges

= diverges

n = 0 \sum \infty (\frac{5}{2})^{n - 1}

k = 0 \sum \infty (0.4)^{k}

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

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

n = 2 \sum \infty \frac{9 n}{ln ( n )}

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