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Evaluate 1+2-3+4+5-6+.....+2005+2006-2007+2008+2009?

Evaluate 1+2-3+4+5-6+.....+2005+2006-2007+2008+2009?

Grade:8

1 Answers

Arun
25763 Points
3 years ago
Dear Nishita
 
It can be written as 
 
 1 + 2 + 3 + 4 + 5 + 6 + 7 +............................. + 2008 + 2009 – [3 + 6 + 9 + 12 + …............+2007]
 ----------------------------------2009 terms----------------------------         ----------------669 terms--------------
 
 = 2009 (2009 + 1)/2   –  669/2 [3 + 2007]
 
 = 2009 * 1005 – 669 * 1005
 
 = 1005 * 134
 
 =  134170

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