Calculation of a power series sum

Question

How can I calculate the following sum:

$$\sum_{n=1}^\infty (n+2)x^n$$

What is wrong with spreading it to: $2x^n + nx^n$? both I know how to calculate. Thank you

There is nothing wrong with that once you know that the sum converges, which it does if and only if $|x|<1$. — J.R., Jan 22 '14 at 17:41

score 0 · Answer 1 · answered Jan 22 '14 at 17:41

0

Nothing wrong. You can use it.

answered Jan 22 '14 at 17:41

score 0 · Answer 2 · answered Jan 22 '14 at 17:42

0

You're absolutely right... as long as you know you're using convergent series !

answered Jan 22 '14 at 17:42

Rivten

2 Answers2