A(x) = sum(n=0 -> infinity) of a(subn)x^n

B(x) = sum(n=0 -> infinity) of b(subn)x^n

A(x) * B(x) = sum(n=0 -> infinity) of a(subn)x^n * sum(n=0 -> infinity) of b(subn)x^n

= sum(k=0 -> infinity) of (a(subk)*b(sub(n-k))x^n (by definition of mulitiplication)

= ?

= sum(k=0 -> infinity) of (b(subk)*a(sub(n-k))x^n

= sum(n=0 -> infinity) of b(subn)x^n * sum(n=0 -> infinity) of a(subn)x^n

= B(x) * A(x)

I can't figure out the missing step... Any advice? Thanks!