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

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

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

n = 2 \sum \infty \frac{1}{n} - \frac{1}{n - 1}

- 1

Solution steps

n = 2 \sum \infty \frac{1}{n} - \frac{1}{n - 1}

Apply Telescoping Series Test:

- 1

= - 1

n = 1 \sum \infty \frac{1}{4 n + 1}

n = 1 \sum \infty (cos (8))^{n}

n = 1 \sum \infty \frac{1}{n ^{9} + 9}

n = 1 \sum \infty \frac{5}{n ^{2} + 4}

n = 0 \sum \infty \frac{n}{3 n ^{2} + 1}

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