Finding coefficient of generating functions I have the equation 
$$(1+x+x^2+\ldots+x^k+\ldots)(1+x^2+x^4+\ldots+x^{2k}+\ldots)(x^2+x^3)$$ 
how of I find the coefficent of $x^{24}$. I know to condense this down to 
$$\frac1{1-x}\cdot\frac1{1-x^2}\cdot x(1+x)$$
but I don't know what to do after that

Hint: There is cancellation, $(1-x^2)=(1-x)(1+x)$. And $x^2+x^3=x^2(1+x)$.
So we end  up with $\dfrac{x^2}{(1-x)^2}$. 
Now everything is straightforward. The coefficients for $\dfrac{1}{(1-x)^2}$ can be found by a direct computation of $(1+x+x^2+\cdots)(1+x+x^2+\cdots)$, or by noticing that $\dfrac{1}{(1-x)^2}$ is the derivative of $\frac{1}{1-x}$, and differentiating $1+x+x^2+x^3+\cdots$ term by term.  
