Establish the binomial series in by means of the following steps. (a) Show that y = (1 + x)α satisfies the initial value problem (1 + x)y′ = αy, y(0) = 1. (b) Show that the power series method gives the binomial series in as the solution of the initial value problem in part (a), and that this series converges if |x| < 1. (c) Explain why the validity of the binomial series given in follows from parts (a) and (b).
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