Question

1999^2-1998^2+1997^2-...-2^2+1^2​

Answer 1

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=

$\dfrac{(3995+3)*999}{2} =\dfrac{3998*999}{2} =1997001$

1²-2²+3²-4²+....+1997²-1998²+1999²==1999²-1997001=1999000

Answer 2

Answer:

675 (6913)

$\div$

$+$