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

The sum from k=1 to infinity of 1/(k(k+1)) is 1

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sum from k=1 to infinity of 1/(k(k+1))

k = 1 \sum \infty \frac{1}{k ( k + 1 )}

1

Solution steps

k = 1 \sum \infty \frac{1}{k ( k + 1 )}

Apply Telescoping Series Test:

1

= 1

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