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back to boardmathematical induction. S(n) = a(1) + a(2) + ... + a(n - 1) + a(n); Plato's conjecture: F(n) = [S(n)]^2; basis: F(1) = [a(1)]^2 = [S(1)]^2 // yes, it holds. induction: F(n) = F(n - 1) + S(n) * a(n) + S(n - 1) * a(n) = [S(n - 1)]^2 + [S(n - 1) + a(n)] * a(n) + S(n - 1) * a(n) = [S(n - 1) + a(n)]^2 = [S(n)]^2 Umm, our conjecture can be renamed as Plato's theorem now. Edited by author 18.04.2019 16:17 |
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