An infinite series question

  • Thread starter Jamin2112
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Homework Statement



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

Homework Equations



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 ∞.
 

Answers and Replies

  • #2
D H
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[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?
So don't do that then. At this stage you have two series, both of which are in terms of xn. The only problem is one starts at n=0 while the other starts at n=1. Can you make them start at the same point?
 

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