Homework Help: Sum of a power series

1. Apr 20, 2014

toothpaste666

1. The problem statement, all variables and given/known data

find the sum of the following series:

$\sum_{n=1}^\infty nx^{n-1} , |x|<1$

2. Relevant equations

$\frac{a}{1-r}$

3. The attempt at a solution

i know that a function representation for that series is $-\frac{1}{(1-x)^2}$ but how is it possible to find the sum of a series with a variable in it? please help :(

Last edited: Apr 20, 2014
2. Apr 20, 2014

micromass

Do you know what

$$\sum_{n=0}^{+\infty} x^n$$

is?

3. Apr 20, 2014

toothpaste666

$\frac{1}{1-x}$

4. Apr 20, 2014

micromass

Now take derivatives.

5. Apr 20, 2014

toothpaste666

i know that the series as a function is $\frac{-1}{(1-x)^2}$ but webassign said that was wrong. they are looking for the sum of the series.

6. Apr 20, 2014

micromass

Yes, it is wrong. Please show your work.

7. Apr 20, 2014

toothpaste666

I wrote it as
$(1-x)^{-1 }$
to take the derivative i multiplied it by the exponent and subtracted one from the exponent.
$-1(1-x)^{-2}$
which is
$-\frac{1}{(1-x)^2}$

8. Apr 20, 2014

toothpaste666

oh wait i see it now. i forgot to use the chain rule. it should be
$\frac{1}{(1-x)^2}$

9. Apr 20, 2014

micromass

Indeed!

10. Apr 21, 2014

thanks!