Chapter 5.1, Problem 17P

To determine

To verify: The equation ${\displaystyle \sum _{k=0}^{\infty }{a}_{k+1}{x}^k}+{\displaystyle \sum _{k=0}^{\infty }{a}_k{x}^{k+1}}={\displaystyle \sum _{k=1}^{\infty }\left(a_{k+1}+a_{k-1}\right)x^k}$ is true.