What is the sum from n=1 to infinity of 1/(n(n+6)) ?

The sum from n=1 to infinity of 1/(n(n+6)) is converges

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sum from n=1 to infinity of 1/(n(n+6))

n = 1 \sum \infty \frac{1}{n ( n + 6 )}

converges

Solution steps

n = 1 \sum \infty \frac{1}{n ( n + 6 )}

Apply Series Comparison Test:

converges

= converges

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What is the sum from n=1 to infinity of 1/(n(n+6)) ?
The sum from n=1 to infinity of 1/(n(n+6)) is converges