Răspunsuri

2014-10-16T15:46:03+03:00
(1+3+5+...+2013)-(2+4+6+...+2012)=
=(2013+1)*[(2013-1):2+1]:2 -  (2012+2)*[(2012-2):2+1]:2=
=2014*1007:2 - 2014*1006:2=
=1007*1007 - 1007*1006=
=1007*(1007-1006)=
=1007

Alta solutie:
(1+3+5+...+2013)-(2+4+6+...+2012)=
=1+ (3-2+5-4+7-6+...+2013-2012)=
=1+(1+1+...+1)= 1+1006=1007
In paranteza "1" se repeta de (2013-3):2+1= 1006 ori ;