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1+2+3+...+2005-1001-1002-...-2006 cel mai rapid raspuns coroana

Răspuns :

   
[tex]1+2+3+...+2005 - 1001-1002-...-2006 = \\ (\underbrace{1+2+3+...+2005}) - (\underbrace{1001+1002+...+2006}) = \\ .~~~~~~~~~~~2005~termeni~~~~~~~~~~~~~~~~~~1006~termeni \\ \\ \displaystyle =\frac{2005(2005+1)}{2} - \frac{1006(2006+1001)}{2} = \\ \\ =\frac{2005 \times 2006}{2} - \frac{1006 \times 3007}{2} = \boxed{2005 \times 1003 - 503 \times 3007}[/tex]



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