(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Rewrite the given expression as a sum whose generic term involves x^{n}

[m=2 to ∞] ∑m(m-1)a_{m}x^{m-2}+ [k=1 to ∞] x∑ka_{k}x^{k-1}

2. Relevant equations

None in this problem

3. The attempt at a solution

To make the first part involve only x^{n}, I can use the substitution n=m-2.

[n=0 to ∞] ∑(n+2)(n+1)a_{n+2}x^{n}.

But I can't make the second part in terms of x^{n}and [n=0 to ∞], as far as I know.

[k=1 to ∞] x∑ka_{k}x^{k-1}= [k=1 to ∞] ∑ka_{k}x^{k}= [n=1 to ∞] ∑na_{n}x^{n}

If I try to take change the start of the sum to n=0, that will effect the x^{n}. See what I'm saying? I want to combine this into one big sum from n=0 to ∞.

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# Homework Help: An infinite series question

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