Answer:1999000
Step-by-step explanation:
1²-2²=(1-2)(1+2)=-1*3=-3
3²-4²=(3-4)(3+4)=-7
5²-6²=(5-6)(5+6)=-11
7²-8²=(7-8)(7+8)=-15
...
1997²-1998²=(1997-1998)(1997+1998)=-3995
1²-2²+3²-4²+....+1997²-1998²+1999²=1999²-(3+7+11+15+...+3995)
Number of terms in the parenthesis: =(3995-3)/(7-3)+1=998+1=999
Parenthesis=
[tex]\dfrac{(3995+3)*999}{2} =\dfrac{3998*999}{2} =1997001[/tex]
1²-2²+3²-4²+....+1997²-1998²+1999²==1999²-1997001=1999000
