The sum of the infinite geometric series 1 + x + x² + x³ + ¼ is well known.
Show that

¥ å n=0  n xn = x (1-x)2

and find

¥ å n=0  n2xn.

Outline a method for finding

¥ å n=0  nkxn

where you do not have to carry out this computation beyond k=2.