## anonymous 5 years ago Use summation given below to find a function that it represents

1. anonymous

$\sum _{n=1}^{\infty } \text{nx}^n$

2. anonymous

$x/(x-1)^2$

3. anonymous

how did you get it?

4. anonymous

give me a second

5. anonymous

I will post this question again

6. anonymous

anything?

7. anonymous

yeah, sorry, busy busy, here it goes

8. anonymous

$\sum_{1}^{∞}n x ^{n} = x * \sum_{1}^{∞}n x ^{n-1} = x * d/dx[\sum_{1}^{∞} x ^{n}] = x * d/dx[1/(1-x)] = x/[(1-x)^{2}]$ Excuse me for the poor formating but the website doesn't offer much of choice. The star (*) stands for multiplication. Thanks.

9. anonymous

Hey there's one catch: correct this: $x * d/dx[\sum_{0}^{n} x ^{n}]$ Because when we differentiate, n->0 not n->1 Thanks