Question

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

Answer 1

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)

=(1/2)×(1/2-1/110)

=27/110