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Digital signal systems problem

The book I am using is "Digital Signal Processing" (Third Edition) by Prokis and Manolakis. It is question 2-45 on page 144.

Consider the system described by the difference equation:

y(n)=a*y(n-1)+b*x(n)
determine b in terms of a so that

THE SUMMATION OF h(n)=1

The limits of the summation are n=- infinity to
n=infinity (I used the term summation instead of the
the mathematical symbol.)

Solution Summary

The solution is in an attachment as a step-by-step equational process.

$2.19