Question 6
The sequence $(a_n)_{n=1}^{\infty}$, with $a_1=a_2=2$, satisfies
$$\frac{2a_{n-1}a_n}{a_{n-1}a_{n+1}-a_n^2}=n^3-n\qquad(n=2,3,4,\ldots).$$
Find the integer closest to $\displaystyle\sum_{n=2}^{2011}\frac{a_{n+1}}{a_n}$.
$$\frac{2a_{n-1}a_n}{a_{n-1}a_{n+1}-a_n^2}=n^3-n\qquad(n=2,3,4,\ldots).$$
Find the integer closest to $\displaystyle\sum_{n=2}^{2011}\frac{a_{n+1}}{a_n}$.