MathDB
TOT 102 1985 Autumn J6 x_{k+1} =x^2_k+x_k, sum 1/{x_i+1}

Source:

August 26, 2019
SequenceSumInteger Partrecurrence relationalgebra

Problem Statement

The numerical sequence x1,x2,..x_1 , x_2 ,.. satisfies x1=12x_1 = \frac12 and xk+1=xk2+xkx_{k+1} =x^2_k+x_k for all natural integers kk . Find the integer part of the sum 1x1+1+1x2+1+...+1x100+1\frac{1}{x_1+1}+\frac{1}{x_2+1}+...+\frac{1}{x_{100}+1}
{A. Andjans, Riga)
Back to ProblemsView on AoPS