If the sum of the coefficients of all even powers of $x$ in the product $\left(1+x+x^2+\ldots x^{2 n

Question

If the sum of the coefficients of all even powers of $x$ in the product $\left(1+x+x^2+\ldots x^{2 n}\right)\left(1-x+x^2-x^3+\ldots+x^{2 n}\right)$ is 61 , then $n$ is equal to

Professor PC Thomas Classes · Answer

Product represents sum of powers. Even powers count sums up to $n$. Solves to $n=30$.