Thread: Power Series Help Please

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

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

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

now simplify