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

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

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

n = 0 \sum \infty \frac{1}{n ( n - 1 )}

1

Solution steps

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

Apply Telescoping Series Test:

1

= 1

\frac{1}{2 r} + \frac{1}{7 r ^{\frac{6}{7}}}

f (x) = \frac{x ^{2} + 11 x + 24}{x + 8}

\frac{d x}{d t} = x

(ln (x - 1))^{^{'}}

y = \frac{x}{( 1 + x ^{2} )}

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