Math Help - String

1. String

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

2. What do you think is the correct answer and WHY?
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3. 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"...?

4. Originally Posted by stapel
Does "find x of that" mean "find the values of x such that"...?
Yes

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

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