2 / 3, - 1,10 / 7, - 17 / 9,26 / 11? | Math enthusiast | Mathematical art

2 / 3, - 1,10 / 7, - 17 / 9,26 / 11?

Let 2 / 3-5 / 510 / 7-17 / 926 / 11-37 / 13 be (- 1) ^ (n + 1) * an / BN, then BN = 2n + 1a2-a1 = 3 = 2 * 1 + 1a3-a2 = 5 = 2 * 2 + 1a4-a3 = 7 = 2 * 3 + 1 An-a (n-1) = 2 (n-1) + 1 add an-a1 = 2 * (1 + 2 +...) +N-1) + 1 * n = n ^ 2A1 = 2An = n ^ 2 + 2, so (- 1) ^ (n + 1) * (n ^ 2 + 2) / (2n + 1)

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