=(1+2+……+4001)/2001
=[(1+4001)+(2+4000)+……+(2000+2002)+2001]/2001
=(4002+4002+……+4002+2001)/2001
=(4002×2000+2001)/2001
=(2001×4000+2001)/2001
=2001×(4000+1)/2001
=4000+1
=4001