Chapter 8.2, Problem 27E

To determine

To show:

The expansion $x^2{\displaystyle \sum _{n=0}^{\infty }n\left(n+1\right)a_n{x}^n}$ is equal to the expansion ${\displaystyle \sum _{n=2}^{\infty }\left(n-2\right)\left(n-1\right)a_{n-2}{x}^n}$.