Let S be a power series (exercise 3.59 ) whose constant term is 1. Suppose we want to find the power series 1/S, that is, the series X such that S · X = 1. Write S = 1 + SR where SR is the part of S after the constant term. Then we can solve for X as follows:
In other words, X is the power series whose constant term is 1 and whose higher-order terms are given by the negative of SR times X. Use this idea to write a procedure invert-unit-series that computes 1/S for a power series S with constant term 1. You will need to use mul-series from exercise 3.60
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