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

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

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

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

2

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Telescoping Series Test:

1

= 2 \cdot 1

Simplify

= 2

x \to 0 lim (+ (\frac{1}{3} + \frac{5}{3 x}))

f (x) = - 2 t^{2} + 3 t - 6

\frac{d}{d x} (\frac{d y}{d x}) + y = 1

\frac{3 s + 2}{s ^{2} + 2 s + 10}

2 a x + b

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