Question

Calculeaza: S=(1+3+5+.....+2013)- (2+4+6+.....+2012)=

Answer 1

S = ( 1 + 3 + 5 + ... + 2013 ) - ( 2 + 4 + 6 + ... + 2012 )

S = ( 1 + 2 + 3 + ... + 2013 ) - [ 2 $*$ ( 1 + 2 + 3 + ... + 1006 ) ]

S = [ (2013 $*$ 2014 : 2) - ( 2 + 4 + 6 + ... + 2012 ) ] - [ 2 [ tex]*[/tex] ( 1006 $*$ 1007 : 2 ) ]

S = { ( 2013 $*$ 1007 ) - [ 2 $*$ ( 1 + 2 + 3 + ... + 1006 ) ] } - [ 2 $*$ ( 1007 $*$ 503 ) ]

S = { 2027091 - [ 2 $*$ ( 1006 $*$ 1007 : 2 ) ] } - ( 2 $*$ 506521 )

S = { 2027091 - [ 2 $*$ ( 1007 $*$ 503 ) ] } - 1013042

S = [ 2027091 - ( 2 $*$ 506521 ) ] - 1013042

S = ( 2027091 - 1013042 ) - 1013042

S = 1014049 - 1013042

S = 1007

Answer 2

Suma devine : S = 1-2 + 3-4 +5-6 +....2013-2012 = (-1) x 1006 + 2013 = 

= 2013-1006 = 1007
Prima suma are 1007 termeni , a doua suma are 1006 termeni.
Rezultatul este verificat!