What is the sum from n=2 to infinity of 1/(n(n+2)) ?

The sum from n=2 to infinity of 1/(n(n+2)) is converges

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sum from n=2 to infinity of 1/(n(n+2))

n = 2 \sum \infty \frac{1}{n ( n + 2 )}

converges

Solution steps

n = 2 \sum \infty \frac{1}{n ( n + 2 )}

Apply Series Comparison Test:

converges

= converges

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f (x) = \frac{1}{x ^{6}}

sec (x) - 6 cos (x)

What is the sum from n=2 to infinity of 1/(n(n+2)) ?
The sum from n=2 to infinity of 1/(n(n+2)) is converges