Power Series Help Please

NotaWiz · Dec 2nd 2007, 12:21 PM

I need to find the power series representation for f(x)= x/(1-2x). I cant seem to figure it out!Any help would be great

**Jhevon** · Dec 2nd 2007, 12:29 PM

Originally Posted by NotaWiz

I need to find the power series representation for f(x)= x/(1-2x). I cant seem to figure it out!Any help would be great

recall that $\frac 1{1 - x} = \sum_0^{\infty} x^n$ for $|x|< 1$

thus, $\frac x{1 - 2x} = \sum_0^{\infty} x \cdot (2x)^n$ for $|x| < \frac 12$

now simplify

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