Establish the binomial series in (12) by means of the
Chapter , Problem 24(choose chapter or problem)
Establish the binomial series in (12) by means of the following steps. (a) Show that y D .1 C x/ satisfies the initial value problem .1 C x/y0 D y, y.0/ D 1. (b) Show that the power series method gives the binomial series in (12) as the solution of the initial value problem in part (a), and that this series converges if jxj < 1. (c) Explain why the validity of the binomial series given in (12) follows from parts (a) and (b).
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