1x2+2x3+3x4+4x5+······98x99+99x100=?

问题描述:

1x2+2x3+3x4+4x5+······98x99+99x100=?

:1×2+2×3+3×4+4×5+……+99×100
=1^2+1+2^2+2+3^2+3+4^2+4+……99^2+99
=(1^2+2^2+3^2+4^2……+99^2)+(1+2+3+4+……+99)
=99×(99+1)×(2×99+1)÷6+(1+99)×99÷2
=33×50(199+3)
=33×1010
=333300