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

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

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

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

- 1

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply Telescoping Series Test:

\frac{1}{2}

= - 2 \cdot \frac{1}{2}

Simplify

- 2 \cdot \frac{1}{2} : - 1

= - 1

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