Rewrite the given expression as a sum whose generic term involves xn
[m=2 to ∞] ∑m(m-1)amxm-2 + [k=1 to ∞] x∑kakxk-1
None in this problem
The Attempt at a Solution
To make the first part involve only xn, I can use the substitution n=m-2.
[n=0 to ∞] ∑(n+2)(n+1)an+2xn.
But I can't make the second part in terms of xn and [n=0 to ∞], as far as I know.
[k=1 to ∞] x∑kakxk-1 = [k=1 to ∞] ∑kakxk = [n=1 to ∞] ∑nanxn
If I try to take change the start of the sum to n=0, that will effect the xn. See what I'm saying? I want to combine this into one big sum from n=0 to ∞.