(1/2+1/3+1/4+1/5+……+1/2007)*(1+1/2+1/3+1/4+……+1/2006)………………

问题描述:

(1/2+1/3+1/4+1/5+……+1/2007)*(1+1/2+1/3+1/4+……+1/2006)………………
计算:(1/2+1/3+1/4+1/5+……+1/2007)*(1+1/2+1/3+1/4+……+1/2006)-(1+1/2+1/3+1/4+……+1/2007)*(1/2+1/3+1/4+^+1/2006)
要求简算

设1/2+1/3+1/4+1/5+.+1/2007为x,1/2+1/3+1/4+.+1/2006为y,得x*(1+y)-(1+x)*y=x+x*y-y-x*y=x-y
(1/2+1/3+1/4+1/5+.+1/2007)-(1/2+1/3+1/4+.+1/2006)=1/2007