Chapter 11.1, Problem 13P

To determine

To show:

That $\sum _{n=2}^{\infty }n\left(n-1\right)a_{n-1}{x}^{n-2}+\sum _{n=1}^{\infty }n{a}_n{x}^{n-1}=\sum _{n=1}^{\infty }\left(n+1\right)\left(n+3\right)a_{n+1}{x}^n$.