Difference between revisions of "2002 OIM Problems/Problem 5"
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The sequence of real numbers <math>a1, a2, \cdots</math> is defined as: | The sequence of real numbers <math>a1, a2, \cdots</math> is defined as: | ||
| − | < | + | <cmath>a_1 = 56, a_{n+1} = a_n - \frac{1}{a_n}</cmath> |
for every integer <math>n \ge 1</math>. | for every integer <math>n \ge 1</math>. | ||
Latest revision as of 03:45, 14 December 2023
Problem
The sequence of real numbers 
is defined as:
![\[a_1 = 56, a_{n+1} = a_n - \frac{1}{a_n}\]](http://latex.artofproblemsolving.com/9/2/0/9201b9360f186cd4e092328a53a591f21f0c32cc.png)
for every integer 
.
Prove that there exists an integer 
, 
, such that 
.
~translated into English by Tomas Diaz. orders@tomasdiaz.com
Solution
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