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Romania National Olympiad 2010 - Grade XI

Source:

April 10, 2011
logarithmslimitreal analysisreal analysis unsolved

Problem Statement

Let a∈R+a\in \mathbb{R}_+ and define the sequence of real numbers (xn)n(x_n)_n by x1=ax_1=a and xn+1=∣xn−1n∣, n≥1x_{n+1}=\left|x_n-\frac{1}{n}\right|,\ n\ge 1. Prove that the sequence is convergent and find it's limit.
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