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

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

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

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

1

Solution steps

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

Apply Telescoping Series Test:

1

= 1

n = 1 \sum \infty \frac{1}{5 + e ^{- n}}

m = 1 \sum \infty \frac{10}{m ^{8} + 3}

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

n = 1 \sum \infty \frac{n}{n ^{2} + 6}

k = 1 \sum \infty \frac{5}{k} - \frac{5}{k + 1}

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