Question

1×2×3+2×3×4+3×4×5+…10×11×12

1×2×3+2×3×4+3×4×5+…10×11×12
有过程

Answer 1

1×2×3+2×3×4+3×4×5+…10×11×12
=(1*2*3*4-0*1*2*3)/4+(2*3*4*5-1*2*3*4)/4+...+(10*11*12*13-9*10*11*12)/4
=10*11*12*13/4
=4290

Answer 2

第n-1项为：(n-1)*n*(n+1) = n*(n^2 -1) = n^3 - n
所以原式
= (2^3 +....+11^3) - (2+...+11)
= (2+3..+11)^2 - 65
= 65*64
=4160

Answer 3

1×2×3+2×3×4+3×4×5+…10×11×12
=(1*2*3*4-0*1*2*3)/4+(2*3*4*5-1*2*3*4)/4+...+(10*11*12*13-9*10*11*12)/4
=10*11*12*13/4
=4290

Answer 4

和是 4290