Assignment:
Consider the real number iteration scheme x_n+1 = f(x_n) for n = 1, 2, ... with x_1 given. In addition, suppose there is a number 0 < p < 1 st lf(x) - f(y)l < = plx-yl for all x,y.
a) Show lx_n+1 - x_nl < = p^n-1lx_2 - x_1l for all n.
b) From this, conclude {x_n}_n is Cauchy.
Provide complete and step by step solution for the question and show calculations and use formulas.