# 1-2 +3-4 +...- 2008 +2009

2010-02-05 04:01:09 +0000 #1

2010-02-05 04:15:41 +0000 #2
by topic get (1-2) + (3-4) + ... ... -2008) +2009 can be obtained (-1) + (-1) + (-1) ... ... +2009, in the middle is a total (2008 / 2) a -1, which is 1004 -1, to be -1,004, -1,004 +2009 = 1005.

Problem-solving ideas: This question in each and every one with a minus sign in formula adding parentheses, obtained a number of less than him a few, that is to be -1, this formula until 2008,2 a number of combinations as a result of -1 of the formula, then by 2008 is to have 1004 such a formula, that is, 1004 -1, that is, -1,004, (1-2 +3-4 +...- 2008) The results of a formula is to -1,004, the last with 2009 to be 1005, what is there do not understand me a message!
2010-02-05 04:32:45 +0000 #3
(1 +1 +1 ........................+ 1) (1005 Items 1)

= 1005

-2 +3 = 3-2 = 1

-4 +5 = 5-4 = 1

and so on.
2010-02-05 04:11:04 +0000 #4
1004

can refer to the law,

1 = 1 1-2 +3 = 1 +1

... ...

1 -2 +3- ... ... +2009 = 1 + (n-1) / 2. . .

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