If $f_{1}=f_{2}=1$ and thereafter $f_{n+2}=f_{n+1}+f_{n}$ for all $n \in N$. Find $\displaystyle\sum_{n=2}^{\infty}\;\large\frac{1}{f_{n+1}\;.f_{n-1}}$

Question

$(a)\;2\qquad(b)\;1\qquad(c)\;\large\frac{1}{2}\qquad(d)\;None\;of\;these$