1×2=1/3 (1×2×3-0×1×2) 2×3=1/3 (2×3×4-1×2×3) 3×4=1/3 (3×4×5-2×3×4) 由以上三个等式相加,可得1×2+2×3+3×4=(1/3)×3×4×5=20 读完以上材料,请你计算(1)1×2+2×3+3×4+…+n×(n+1)=
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(1)1×2+2×3+3×4+…+n×(n+1)= (1/3)n(n+1)(n+2)
(2)1×2+2×3+3×4+…+10×11= 1/3 (12×3-0×1×2) +1/3 (2×3×4-1×2×3)+…………+1/3(10x11x12-9x8x7)=1/3（10x11x12-0x1x2)=440
(3) .1260
======以下答案可供参考======
供参考答案1:
(1)(1/3)*(n+1)*(n+2)
(2)(1/3)*10*11*12=440
(3)规律(1/4)*n*(n+1)*(n+2)*(n+3) 因此答案为(1/4)*7*8*9*10=1260
供参考答案2:
(1)1×2+2×3+3×4+…+n×(n+1)=_(n+1)(n+2)/3____ (2)1×2+2×3+3×4+…+10×11=(11+1)11_/3=44____(写出过程) (3)1×2×3+2×3×4+3×4×5+…+7×8×9=__180____