MathDB
Problem 8 of First round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 21, 2018
algebrarecurrence relationrecursion

Problem Statement

The row x1,x2,…x_1, x_2,… is defined by the following recursion
x1=1x_1=1 and xn+1=xn+xnx_{n+1}=x_n+\sqrt{x_n}
Prove that
∑n=120181xn<3\sum_{n=1}^{2018}{\frac{1}{x_n}}<3.
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