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--- pow:problem6f21 [2021/11/21 04:37] – created mazur
+++ pow:problem6f21 [2021/11/23 17:52] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange| Problem 6 (due Monday, November 22)>
+Let $a_1=3/2$ and $a_{n+1}=a_n^2-a_n+1$. Compute the sum
+\[ \frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+\ldots .\]
+</box>
+Two solutions were received: from Ashton Keith and Pluto Wang. Both solvers show that if $a_1=a>1$ then
+the infinite sum is equal to 1/(a-1). Pluto's solution is essentially the same as our original solution.
+Ashton's solution is based on the same idea, but used slightly differently, and some claims are not justified with sufficient rigor. For more details see the following link {{:pow:2021fproblem6.pdf|Solution}}.