# Math Help - Contest problem 2

1. ## Contest problem 2

What is the value of the expression: 1-2-3+4-5+6-7+8-.....-2011+2012?

2. ## Re: Contest problem 2

Originally Posted by Kanwar245
What is the value of the expression: 1-2-3+4-5+6-7+8-.....-2011+2012?
1-2-3+4 = 0
-5 + 6 = 1
-7 + 8 = 1 ....continue

OK?

3. ## Re: Contest problem 2

Originally Posted by Kanwar245
What is the value of the expression: 1-2-3+4-5+6-7+8-.....-2011+2012?
I think that you have some sign errors in the statement of the question.

$\sum\limits_{k = 1}^N {\left( {2k - 1} \right)} = N(N + 1) - N = {N^2}$

$\sum\limits_{k = 1}^N {\left( {2k } \right)} = N(N + 1) = {N^2+N}$

4. ## Re: Contest problem 2

If no sign errors: (2012-4) / 2 - 1004

If -1+2-3+4-5+6....: 2012 / 2 = 1006 (net of 1 per pairs)

5. ## Re: Contest problem 2

No there are no sign errors, so ans is 1004