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}

Expand

(\frac{n}{n + 2})^{2} : \frac{n ^{2}}{n ^{2} + 4 n + 4}

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

Apply Series Divergence Test:

diverges

= diverges

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