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Clever calculation: how to calculate 1 × 2 + 2 × 3 + 3 × 4 +... + 49 × 50? How to calculate 1 × 2 + 2 × 3 + 3 × 4 +... + 49 × 50
Answer: 41650 in general, let s = 1 * 2 + 2 * 3 + 3 * 4 + N * (n + 1) then 3S = 1 * 2 * 3 + 2 * 3 * 3 + 3 * 4 * 3 + 4 * 5 * 3 + n*(n+1)*3 =1*2(3-0)+2*3(4-1)+3*4(5-2)+…… n(n+1)[n+2-(n-1)] =1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+…… +N (n + 1) (n + 2) - (n-1) n (n + 1) = n (n + 1) (n + 2), so the original formula = s = n (n + 1) (n + 2) / 3, so s = 49 * (49 + 1) * (49 + 2) / 3 = 41650
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