简便运算1990/1990*1991+1990/1991*1992+.+1990/2001*2002=

问题描述:

简便运算1990/1990*1991+1990/1991*1992+.+1990/2001*2002=

(1/1990*1991+1/1991*1992+.+1/2001*2002)×1990 =(1/1990-1/1991+1/1991-1/1992+.+1/2001-1/2002)×1990 =1-1990/2002=1-995/1001=6/1001