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

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

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

n = 1 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

1

Solution steps

n = 1 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

Apply Telescoping Series Test:

1

= 1

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