Thread: How Good Are You At Reasoning?

Originally Posted by Xei

Have you stumbled across any puzzles yourself for a lay audience?

Haven't been looking. One interesting extension to (2) would be to determine for which integers, n, some real x exists with x + 1/x = n. One could then prove that as n -> infinity, x/n approaches 1. This is more amateur mathematician stuff than "lay audience" friendly though. If we let x(n) be such that x(n) + 1/x(n) = n, and let w_n(k) = x(n)^k + 1/x(n)^k, then it might be interesting to explore the sequences w_n(k) as k tends to infinity. Right now we just have the recurrence formula w_n(k) = w_n(k - 1)n - w_n(k - 2).