1949^2-1950^2+1951^2-1952^2+……+1997^2-1998^2 +1999^2
=(1949^2-1950^2)+(1951^2-1952^2)+……+(1997^2-1998^2) +(2000 -1)^2
=(1949+1950)(1949-1950)+(1951+1952)(1951-1952)+……+(1997+1998)(1997-1998) +4000000-4000+1
=(1949+1950)(-1)+(1951+1952)(-1)+……+(1997+1998)(-1) +3 996 001
=-(1949+1950+1951+1952+……+1997+1998) +3 996 001
=-(1949+1998)*50/2 +3 996 001
=-3947*25 +3 996 001
=-98675 +3 996 001
=3897326