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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Originally Posted by Apprentice123 Find x of that $\displaystyle x+2x^2+3x^3+4x^4+...=3$, with $\displaystyle |x|<1$ and $\displaystyle x \neq 0$ Does "find x of that" mean "find the values of x such that"...?
Originally Posted by stapel Does "find x of that" mean "find the values of x such that"...? Yes
$\displaystyle x+2x^2+3x^3+4x^4+\cdots = \sum_{n=1}^{\infty} nx^n$ It can be shown that this is the power series for the function: $\displaystyle f(x)= \frac{x}{(1-x)^2} \qquad |x| < 1$
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