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)=(2)1×2+2×3+3×4+…+10×11=

Question

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)=_____ (2)1×2+2×3+3×4+…+10×11=_____(写出过程) (3)1×2×3+2×3×4+3×4×5+…+7×8×9=______

Answer 1

(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