Find x of that $\displaystyle x+2x^2+3x^3+4x^4+...=3$, with $\displaystyle |x|<1$ and $\displaystyle x \neq 0$

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- Mar 23rd 2009, 02:41 PMApprentice123String
Find x of that $\displaystyle x+2x^2+3x^3+4x^4+...=3$, with $\displaystyle |x|<1$ and $\displaystyle x \neq 0$

- Mar 23rd 2009, 03:18 PMPlato
What do you think is the correct answer and WHY?

Show us you are really interested in learning something. - Mar 23rd 2009, 03:25 PMstapel
- Mar 23rd 2009, 04:04 PMApprentice123
- Mar 23rd 2009, 05:04 PMo_O
$\displaystyle x+2x^2+3x^3+4x^4+\cdots = \sum_{n=1}^{\infty} nx^n$

It can be shown that this is the power series for the function: $\displaystyle f(x)= \frac{x}{(1-x)^2} \qquad |x| < 1$