Problem-Solving Strategies Ch 9 Problem 25

Engel 9.25. The sequence x_n is defined by x_1 = 1/2, x_{k+1} = x_k^2 + x_k. Find the integer part of the sum

\displaystyle\frac{1}{x_1 + 1} + \frac{1}{x_2+1} + \dots + \frac{1}{x_{100}+1}.

Note: This problem was taken from Arthur Engel’s Problem-Solving Strategies.

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