Similar questions:/kloc-0 /× 2+2× 3+…+n (n+1) =?

Observe the following three special equations:

1×2 = n( 1×2×3-0× 1×2)

2×3=x(2×3×4- 1×2×3)

3×4=n(3×4×5-2×3×4)

Adding the two sides of these three equations, we can get 1×2+2×3+3×4=m×3×4×5=20.

According to the result of adding three special equations, it can be solved by substituting them into the memory for calculation.

)∫ 1×2+2×3+3×4 = m×3×4×5 = 1/3×4×5 = 20

∴ 1×2+2×3+…+ 100× 10 1= 1/3× 100× 10 1× 102=343400