怎么巧算2000乘2002乘(2000之1乘2001之1加2001之1乘2002之1？

2000*2000*（1/(2000*2001)+1/(2001*2002))

=2000*2000*(1/2000-1/2001+1/2001-1/2002)

=2000*2000*(1/2000-1/2002)

=2000*2000*(2/(2000*2002))

=2000*2000*2/2000/2002

=2000/1001

2000*2002*[(1/2000)*(1/2001)+(1/2001)*(1/2002)]

=2000*2002*(1/2001)*(1/2000+1/2002)

=2000*2002*(1/2001)*(2002+2000)/(2000*2002)

=(2002+2000)/2001

=4002/2001

=2