Question 7
Suppose
$$
n(n+1) a_{n+1} = n(n-1) a_n - (n-2) a_{n-1}
$$
for every positive integer $n \geq 1$.
Given that $a_0 = 1$, $a_1 = 2$, find
$$
\frac{a_0}{a_1} + \frac{a_1}{a_2} + \frac{a_2}{a_3} + \cdots + \frac{a_{50}}{a_{51}}.
$$
$$
n(n+1) a_{n+1} = n(n-1) a_n - (n-2) a_{n-1}
$$
for every positive integer $n \geq 1$.
Given that $a_0 = 1$, $a_1 = 2$, find
$$
\frac{a_0}{a_1} + \frac{a_1}{a_2} + \frac{a_2}{a_3} + \cdots + \frac{a_{50}}{a_{51}}.
$$