MathDB

a_0, a_1, \ldots, a_{100}

and

b_1, b_2,\ldots, b_{100}

are sequences of real numbers, for which the property holds: for all

n=0, 1, \ldots, 99

, either a_{n+1}=\frac{a_n}{2} \text{and} b_{n+1}=\frac{1}{2}-a_n, or a_{n+1}=2a_n^2 \text{and} b_{n+1}=a_n. Given

a_{100}\leq a_0

, what is the maximal value of

b_1+b_2+\cdots+b_{100}

Problem Statement