Question

x+3x+5x+..........+2011x=2x+4x+6x+...........+2010x+2012 cum se calculeaza?

Answer 1

X+3x+5x+...+2011x=scot x factor si calculez suma
X(1+3+5+...+2011)=(1+2011)+(3+2009)+(5+2007)+......+(1005+1007)=
2012+2012+....+2012=2012*503=1012036

sunt 2012/2=1006 nr deci 1006/2=503 sume de 2012


2X+4x+6x+...+2010x=scot x factor si calculez suma
X(2+4+6+...+2010)=(2+2010)+(+2008)+(6+2006)+......+(1004+1008)+1006=
2012+2012+....+2012+1006=2012*502+1006=1011030

sunt 2010/2=1005 nr deci 1005/2=502 sume de 2012 si ala din mijloc nu are pereche


deci ec este 1012036x=1011030x+2012
1012036x-1011030x=2012
1006x=2012
x=2