What is the difference between the sum of all even numbers and the sum of all odd numbers from 0 through 1000?

Question

anonymous · Answer

even  $$n^2+n$$
odd $$n^2$$

aravindg · Answer

sum of even numbers till 1000 - sum of odd numbers till 1000

= (2 + 4 + 6 + ... + 1000) - (1 + 3 + 5 + ... + 999) 

=2 + 4 + 6 + ... + 1000 - 1 - 3 - 5 - ... - 999

=2 - 1 + 4 - 3 + 6 - 5 + ... + 1000 - 999

=(2 - 1) + (4 - 3) + (6 - 5) + ... (1000 - 999)

Does this help ??

anonymous · Answer

Not really....

hero · Answer

^Yes, @AravindG is on the right track

aravindg · Answer

why not ? what doubt do you have in my working?

hero · Answer

The difference increases by 5 every 10 units

anonymous · Answer

So it's 500? That's hard to understand...

anonymous · Answer

$$1000=2k-1 ,1000=2k \implies k=500 $$
difference
$$n^2+n-n^2=n$$
500

anonymous · Answer

Ah. Thanks!

hero · Answer

Great job everyone