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

Apply Telescoping Series Test:

- 1

= - 1

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

n = 0 \sum \infty \frac{6}{n}

i = 1 \sum \infty e^{- i}

n = 1 \sum \infty \frac{( - 3 + 2 ) ^{n}}{n}

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

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