Find Maclaurin series for$f(x) = \frac{2x}{1-5x^3}$ I'm trying to find the Maclaurin series for $f(x) = \frac{2x}{1-5x^3}$, but my solution is different from what I know it supposed to be, which is $2x+10x^4+50x^7+250x^{10}+...$
This is my attempt:  
$$f(x) = \frac{2x}{1-5x^3}$$
$$\frac{1}{1-x} = 1+x+x^2+x^3+...$$ 
$$\frac{2x}{1-x}=2x+2x^2+2x^3+2x^4+...\tag{multiply both sides by $x$}$$
$$\frac{2x}{1-5x^3}=10x^3+50x^6+250x^9+625x^{12}+...\tag{substitute $x$ with $5x^3$}$$
Where is my mistake?

Your problem is that you should first substitute, then multiply. Else, you're forgetting to substitute in the $2x$ term.
