Question

calculati : (2+4.....+2012) -(1+3.....+2011) . urgentttttttt!!!!!!

Answer 1

ai de aplicar 2 formule

2+4+...+2012 = 2(1+2+3+....+1006) 
Gauss in paranteza
1006*1007/2  

2* 1006*1007/2 = 1006*1007

si pentru a doua ai alta formula 

1+3+....+2011 = 
1+3+5+...+2n-1 = n*n
in cazul nostru ultimul termen este 2011
2n-1=2011
2n=2012
n=1006

asadar a doua paranteza va fi egal cu 1006*1006

le punem cap la cap

1006*1007-1006*1006 = 
1006*1007-1006^2 =
1006(1007-1006) =
  1006*1 = 1006

Answer 2

S= (2+4.....+2012)= 2*(1+2+3+....+1006)= 2*1006*1007/2=1013042

 
S=(1+3.....+2011)=  n*n=n²= 1006²

2n - 1= 2011
2n= 2012
n=1006

(2+4.....+2012) -(1+3.....+2011)= 2*1006*1007/2 -1006*1006=
= 1006*(2*1007/2 -1006)= 1006*(1007-1006)=1006*1=1006