Positive integers
Source: Canadian Mathematical Olympiad 1976 Problem 2
October 23, 2008
algebra proposedalgebra
Problem Statement
Suppose
n(n\plus{}1)a_{n\plus{}1}\equal{}n(n\minus{}1)a_n\minus{}(n\minus{}2)a_{n\minus{}1}
for every positive integer . Given that a_0\equal{}1,a_1\equal{}2, find
\frac{a_0}{a_1}\plus{}\frac{a_1}{a_2}\plus{}\frac{a_2}{a_3}\plus{}\dots\plus{}\frac{a_{50}}{a_{51}}.