Question

Calculati:
2-4+6-8+10-12+....2014-2016=

dau 15 puncte

Answer 1

2-4+6-8+10-12+....2014-2016

=2[(1-2)+(3-4)+(5-6)+.........+(1007-1008)]

=2(-1-1-1...........-1); sunt 1008:2=504 perechi de doua nr, deci 504 de -1

=2· (-1)·504

=-1008

Answer 2

2 - 4 + 6 - 8 + 10 - 12 +...+ 2014 - 2016 =

nr de termeni pozitivi  (2014-2):(6-2)+1=2012:4+1=503+1=504

nr de termeni negativi  (2016-4):(8-4)+1=2012:4+1=503+1=504

daca le grupam 2 cate 2 vom obtine 504 rezultate =  - 2

2 - 4 + 6 - 8 + 10 - 12 +...+ 2014 - 2016 =  504 × (-2)=  - 1008