CMO 1976 Problem 2

Suppose $$n(n+1)a_{n+1}=n(n-1)a_n-(n-2)a_{n-1}$$ for every positive integer $n\ge1$ . Given that $a_0=1,a_1=2$ , find $$\frac{a_0}{a_1}+\frac{a_1}{a_2}+\frac{a_2}{a_3}+\dots+\frac{a_{50}}{a_{51}}.$$