Tell me hint, $\sum ^{\infty }_{n=1}\dfrac{i}{\left( n+1\right) \left( n+2\right) }$

Question

I want to solve this. $$\sum ^{\infty }_{n=1}\dfrac{i}{\left( n+1\right) \left( n+2\right) }$$ Answer is $\dfrac{i}{2}$.

I don't know how to solve this. Please tell me hint.

Answer 1

Hint: $$ \frac{1}{(n+1)(n+2)} = \frac{1}{(n+1)}-\frac{1}{(n+2)} $$