Question: Prove that the error of the bisection method is given by the expression |r-c_n|2^-n(b-a). where [a_0,b_0],...,[a_n,b_n] denote the intervals of the bisection method, r=lim n

Prove that the error of the bisection method is given by the expression |r-c_n|2^-n(b-a). where [a_0,b_0],...,[a_n,b_n] denote the intervals of the bisection method, r=lim n to infinity c_n is a root, and c_n=1/2(a_n+b_n)

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