Question

sa se afle
1 +2+3-4+5+6+7-8+2009+2010+2011-2012

Answer 1

1 +2+3-4+5+6+7-8+2009+2010+2011-2012=8078

Answer 2

Banuiesc ca este vorba de urmatorul exercitiu:
1+2+3-4+5+6+7-8+...+2009+2010+2011-2012=
Observam ca daca adunam si apoi scadem:
4+8+...+20012
obtinem:
1+2+3+4+5+6+7+8+...+2009+2010+2011+2012-2(4+8+...+2012)=
Observam ca avem o Suma Gauss, iar in paranteza putem da factor comun 4:
1+2+3+4+5+6+7+8+...+2009+2010+2011+2012-8(1+2+...+503)=
Observam ca am reusit sa punem in evidenta o a doua Suma Gauss.
Scriem expresiile celor doua Sume Gauss:
2012(2012+1)/2-8·503(503+1)/2=2012·2013/2-8·503·504/2= 1006·2013-4·503·504=2025078-1014048=1011030 
Sper ca ti-am fost de ajutor. Spor la lucru!