#1**+1 **

This problem is pretty simple if we think about it in a different way.

We see the we have 1 - 2 + 3 - 4 +... + 2005 - 2006 + 2007 - 2008 + 2009 - 2010.

It looks hard, but all we have to see are the -1.

**1-2 is equal to -1, 3-4 is equal to -1, and so on.**

Now, all we have to do is figure out how many -1 s we have.

the biggest number is 2010, and if we divide that by 2, (because every two numbers is a -1) we get 1005.

From this, we can conclude that the answer is -1*1005=**-1005**

mathisopandcool May 2, 2021