用简便算法计算:(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1/2-1/3-1/4-…-1/2010)

问题描述:

用简便算法计算:(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1/2-1/3-1/4-…-1/2010)
(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)

(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)=(1-1/2-1/3-1/4-…-1/2010)×[(1/2+1/3+1/4+…+1/2010)-(1/2+1/3+1/4+…+1/2010)]=(1-1/2...