Question

Prove
\[ \sum_{n=1}^\infty \frac { n(n+1)}{2^n} =8 \]

Hint: Use \[ \sum_{n=0}^\infty \ x^n =\frac 1 {1-x}, \quad |x|<1 \]

and use the term by term differentiation method.
Of course, I know how to do it. I am sure some f you can. Give it a try.

Answer 1

Hint: Use \[ \sum_{n=0}^\infty x^n =\frac 1 {1-x}, \quad |x|<1 \]

and use the term by term differention method.
Of course, I know hoow to do it. I am sure some of you can. Give it a try.