Question 13
A sequence $(a_n)_{n=1}^{\infty}$ has $a_1=a_2=2$ and, for all $n=2,3,4,\ldots$,
$$\frac{2a_{n-1}a_n}{a_{n-1}a_{n+1}-a_n^2}=n^3-n.$$
Find the integer closest to $\displaystyle\sum_{k=2}^{2011}\frac{a_{k+1}}{a_k}$.
$$\frac{2a_{n-1}a_n}{a_{n-1}a_{n+1}-a_n^2}=n^3-n.$$
Find the integer closest to $\displaystyle\sum_{k=2}^{2011}\frac{a_{k+1}}{a_k}$.