Question

Calculați 1-2+3-4+5-6+........+2013-2014

Answer 1

O metoda :
1-2+3-4+5-6+........+2013-2014  =
= -1 -1-1 ....... -1     (de 2014/2  ori )
= -1007

O alta metoda :
1-2+3-4+5-6+........+2013-2014 =
1+3+5+....+2013 - 2 - 4 - ... -2014 =
1+2+3+4+....+2013 - 2(1+2+.....1007)=
2013*2014/2 - (2+4+.....2012)  - 2(1+2+....+1007)=
2013*1007 - 2(1+2+3+...+1006)-2*1007*1008/2 =
2013*1007 - 2*1006*1007/2 - 2*1007*1008/2 =
2013*1007 - 1006*1007- 1007*1008 =
1007*(2013-1006-1008)=
1007 * (-1)= -1007