Hi, this question involves finding an explicit formula for the given f(x):

$\displaystyle f(x)=1+2x+x^2+2x^3+x^4+....$ that is, its coefficients are $\displaystyle c_{2n=1}$ and $\displaystyle c_{2n+1}=2$ for all $\displaystyle n\geq0$

However, I only knw how to work from the formla to get the power series but not otherwise. Please help.

The answer is $\displaystyle f(x)=\frac{1+2x}{1-x^2}$