一道数学题 简算1/1× 2× 3+1/2×3×4+1/3×4×5+······+1/9×10×11=?

问题描述:

一道数学题 简算1/1× 2× 3+1/2×3×4+1/3×4×5+······+1/9×10×11=?

1/1×2×3=(1/2)×(1/1×2-1/2×3)1/2×3×4=(1/2)×(1/2×3-1/3×4)……1/9×10×11=(1/2)×(1/9×10-1/10×11)所以原式=(1/2)×(1/1×2-1/2×3+1/2×3-1/3×4……+1/9×10-1/10×11)=(1/2)×(1/1×2-1/10×11)=(1/...