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Compute 1 - 2 + 3 - 4 +... + 2005 - 2006 + 2007 - 2008 + 2009 - 2010.

 May 1, 2021
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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

 

 

 

cheeky

 May 2, 2021
edited by mathisopandcool  May 2, 2021

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