What is the sum from n=1 to infinity of 2/(5n^2+5n) ?

The sum from n=1 to infinity of 2/(5n^2+5n) is 2/5

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sum from n=1 to infinity of 2/(5n^2+5n)

n = 1 \sum \infty \frac{2}{5 n ^{2} + 5 n}

\frac{2}{5}

Decimal

0.4

Solution steps

n = 1 \sum \infty \frac{2}{5 n ^{2} + 5 n}

Apply the constant multiplication rule:

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

= 2 \cdot n = 1 \sum \infty \frac{1}{5 n ^{2} + 5 n}

Apply Telescoping Series Test:

\frac{1}{5}

= 2 \cdot \frac{1}{5}

Simplify

2 \cdot \frac{1}{5} : \frac{2}{5}

= \frac{2}{5}

What is the sum from n=1 to infinity of 2/(5n^2+5n) ?
The sum from n=1 to infinity of 2/(5n^2+5n) is 2/5