Answer
$$\sum^{\infty}_{n=0} (n+2)(n+1)a_{n+2}x^{n}$$
Work Step by Step
1. Substitute each $n$ in the expression for a $n+2$:
$$\sum^{\infty}_{n+2=2} (n+2)(n+2-1)a_{n+2}x^{n+2-2}$$ $$\sum^{\infty}_{n=0} (n+2)(n+1)a_{n+2}x^{n}$$
Elementary Differential Equations and Boundary Value Problems 9th Edition
by Boyce, William E.; DiPrima, Richard C.
Published by
Wiley
ISBN 10:
0-47038-334-8
ISBN 13:
978-0-47038-334-6
Chapter 5 - Series Solutions of Second Order Linear Equations - 5.1 Review of Power Series - Problems - Page 249: 21
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