# Faraz's reciprocal sequence

Algebra Level 5

Consider the sequence $$\{a_i\}_{i\geq0}$$ such that $$a_0=\sqrt{7}+1$$ and $$a_{n+1}=a_n^2-a_n+1$$. The sum $\sum_{i=0}^{\infty} \frac{1}{a_n},$ can be written as $$\frac{1}{\sqrt{b}}$$. What is the value of $$b$$?

This problem is shared by Faraz M. from AMSP.

×