Find the function, f(x), which the infinite series
1-(x^3)+(x^6)-(x^9)+(x^12)-(x^15)+....... converges to.
The hint is "What is 1-x+(x^2)-(x^3)+(x^4)-(x^5)+....."
I know that 1-x+(x^2)-(x^3)+(x^4)-(x^5)+.... sums to 1/(1+x) for lxl<1 because it is the derivative of the taylor series for ln(1+x) but all I can think of to use that hint is that f(x)=(1/(1+x))+x-(x^2)-(x^4)+(x^5)+(x^7)-(x^8)-(x^10)+(x^11)+.... which doesn't help me much (as far as I can tell).