Thread: Multiplication of series

1. Multiply the series for (1-x)^-1 (valid when |x|<1) by itself and so obtain the expansion

(1-x)^-2 = sigma n=0 to infinity (n+1)x^n, |x|<1.

2. Derive the expansion

(1-x)^-3 = sigma n=0 to infinity ((n+1)(n+2)*x^n)/2 (|x|<1)

by multiplication of series. Use the result of Exercise 1.

Multiplying series is extra work in this case.

Notice that and ...

is absolutely convergent for . Use a well known result about Cauchy product of series.


Fernando Revilla