Separating similar terms

Algebra Level 2

What is 1-2+3-4+5-6+...+2013-2014?


The answer is -1007.

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April Queen Piedad by April Queen Piedad , 29, Philippines

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3 solutions

Akash Gupta
Jan 31, 2015

we can make pairs.
(1-2+(3-4)+...+(2013-2014)
it results to
(-1)+(-1)...(2014/2 times)
So,
-1 X 1007 =-1007


2 Helpful 0 Interesting 0 Brilliant 0 Confused

1 − 2 + 3 − 4 + . . . + 2013 − 2014 1 - 2 + 3 - 4 + ... + 2013 - 2014

= ( 1 − 2 ) + ( 3 − 4 ) + . . . + ( 2013 − 2014 ) = (1-2) + (3-4) + ... + (2013 - 2014)

= ( − 1 ) + ( − 1 ) + . . . ( − 1 ) ⏟ 1007 times \underbrace{= (-1) + (-1) + ... (-1)}_\text{1007 times}

= − 1007 = -1007

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Lu Chee Ket
Jan 31, 2015

-2014/ 2 = - 1007

Evaluated using Excel.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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