Question 40
A sequence is defined by $A_{0}=0$, $A_{1}=1$, $A_{2}=2$, and, for integers $n \geq 3$,
$$
A_{n}=\frac{A_{n-1}+A_{n-2}+A_{n-3}}{3}+\frac{1}{n^{4}-n^{2}}
$$
Compute $\lim _{N \rightarrow \infty} A_{N}$.
$$
A_{n}=\frac{A_{n-1}+A_{n-2}+A_{n-3}}{3}+\frac{1}{n^{4}-n^{2}}
$$
Compute $\lim _{N \rightarrow \infty} A_{N}$.