1999^2-1998^2+1997^2-...-2^2+1^2​

675 (6913)

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=

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

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: