Question 1050865
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<pre>
Group the numbers in the series in pairs:

1 - 2 + 3 - 4 + 5 - 6 + . . . + 2013 = 

(1-2) + (3-4) + (5-6) + . . . + (2011-2012) + 2013

The last number, 2013, is without pair.

Notice that every difference in parentheses is equal to -1.

How many pairs do you have ?  {{{2012/2}}} = 1006.

So, you have the sum of 1006 terms of "-1" plus 2013, which is -1006 + 2013.

Add the last two numbers.

And compare with the answer.
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Solved.


This problem is actually for low grade (young !) students who may not know about the sum of arithmetic progression.


This problem is to develop their combinatoric skills.