-1+2-3+4-5+6...-995+996-997+998-999+1000
break up this sequence into two sequences
-1-3-5-7-...-993-995-997-999 and 2+4+6+8+...+994+996+998+1000
S(500)=(500/2)(2[-1]+[500-1][-2])
S(500)=(250)(-2+[499][-2])
S(500)=(250)(-2+[-998])
S(500)=(250)(-1000)
S(500)=-250,000
S(500)=(500/2)(2[2]+[500-1]2)
S(500)=(250)(4+[499]2)
S(500)=(250)(4+998)
S(500)=(250)(1002)
S(500)=250,500
add the two results
250,500+(-250,000)=500 for the value of the sequence
If you want to use simple arithmetic, do the following...
-1+(-999)=-1000
-3+(-997)=-1000
-5+(-995)=-1000
and so on
you have 250 of these sums
250*(-1000)=-250,000
then...
2+1000=1002
4+998=1002
6+996=1002
and so on
you have 250 of these sums
250*1002=250,500
250,500+(-250,000)=500 for the value of the sequence
Christopher S.
(−1+2−3+4−?+1000)===((−1+2)+(−3+4)+?+(−999+1000))(1+1+?+1)500
Therefore, the answer is 4⋅500=(E) 2000.
11/11/15