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

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

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

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

1

Solution steps

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

Apply Telescoping Series Test:

1

= 1

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\int \frac{x ^{2} + 3 x - 1}{x ^{3} + 8} d x

\int x 6 1 + x^{2} d x

\int \frac{cos ( \frac{π}{2} )}{x ^{2}} d x

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