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Telescoping & Recursion · Challenge problem

A sequence is defined by a1=54a_1 = \dfrac{5}{4} and an+1=an2−an+1a_{n+1} = a_n^2 - a_n + 1 for n≥1n \ge 1. What is ∑n=1∞1an\displaystyle\sum_{n=1}^{\infty} \frac{1}{a_n}?