What is the sum from n=0 to infinity of 1/(n^2-n) ?

The sum from n=0 to infinity of 1/(n^2-n) is 1

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sum from n=0 to infinity of 1/(n^2-n)

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

1

Solution steps

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

Apply Telescoping Series Test:

1

= 1

n = 1 \sum \infty \frac{7}{5 ^{n}}

n = 1 \sum \infty \frac{1 ^{n}}{n !}

n = 1 \sum \infty \frac{1}{4 n ^{2} - 25}

m = 2 \sum \infty \frac{2}{7 ^{m}}

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

What is the sum from n=0 to infinity of 1/(n^2-n) ?
The sum from n=0 to infinity of 1/(n^2-n) is 1