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1x2×3十2x3x4十3x4X5+…十9X10x11的值是的少

1×2+2×3+3×4+...+n×(n+1) = (1/3)×[1×2×3 - 0×1×2] +(1/3)×[2×3×4 - 1×2×3] +(1/3)×[3×4×5 - 2×3×4] +... +(1/3)×[n×(n+1)×(n+2) - (n-1)×n×(n+1)] = (1/3)×n×(n+1)×(n+2) [2] 相邻三个正整数乘积和 1×2×3+2×3×4+3×4×5+...+n×(n+1)×...

5/(2*3*4) = 1/(2*4) + 1/(3*4) = 1/2 *( 1/2 - 1/4) + ( 1/3 - 1/4) 7/(3*4*5) = 1/(3*5) + 1/(4*5) = 1/2 *(1/3 - 1/5) + (1/4 - 1/5) 9/(4*5*6) = 1/(4*6) + 1/(5*6) = 1/2 *(1/4 - 1/6) + ( 1/5 - 1/6) 11/(5*6*7) = 1/(5*7) + 1/(6*7) = 1/...

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