Answer: Show that

Chapter 8, Problem 28E

(choose chapter or problem)

28. Show that

\(2 \sum_{n=0}^{\infty} a_{n} x^{n+1}+\sum_{n=1}^{\infty} n b_{n} x^{n-1}\)

\(=b_{1}+\sum_{n=1}^{\infty}\left[2 a_{n_{1}}+(n+1) b_{n+1}\right] x^{n}\)

Equation transcription:

Text transcription:

2 sum{n=0}^{infty} a{n} x^{n+1}+sum{n=1}^{infty} n b{n} x^{n-1}

=b{1}+sum{n=1}^{infty}[2 a{n{1}}+(n+1) b{n+1}] x^{n}