Question

Use summation given below to find a function that it represents

Answer 1

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

Answer 2

\[x/(x-1)^2\]

Answer 3

how did you get it?

Answer 4

give me a second

Answer 5

I will post this question again

Answer 6

anything?

Answer 7

yeah, sorry, busy busy, here it goes

Answer 8

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

Answer 9

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