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1977 Canadian MO Problems/Problem 6

Revision as of 14:13, 7 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Let <math>0<u<1</math> and define <cmath>u_1=1+u\quad ,\quad u_2=\frac{1}{u_1}+u\quad \ldots\quad u_{n+1}=\frac{1}{u_n}+u\quad ,\quad n\ge 1</cmath> Show that ...")
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Problem

Let $0<u<1$ and define \[u_1=1+u\quad ,\quad u_2=\frac{1}{u_1}+u\quad \ldots\quad u_{n+1}=\frac{1}{u_n}+u\quad ,\quad n\ge 1\] Show that $u_n>1$ for all values of $n=1,2,3\ldots$.

Solution

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