String

**Apprentice123** · March 23rd 2009, 02:41 PM

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

**Plato** · March 23rd 2009, 03:18 PM

What do you think is the correct answer and WHY?
Show us you are really interested in learning something.

**stapel** · March 23rd 2009, 03:25 PM

Originally Posted by Apprentice123

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

Does "find x of that" mean "find the values of x such that"...?

**Apprentice123** · March 23rd 2009, 04:04 PM

Originally Posted by stapel

Does "find x of that" mean "find the values of x such that"...?

Yes

**o_O** · March 23rd 2009, 05:04 PM

$x+2x^2+3x^3+4x^4+\cdots = \sum_{n=1}^{\infty} nx^n$

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

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