Question

Sa se calculeze sumele :
2005+2+4+...+4008
1996+2+4+...+3990

Answer 1

2005+2+4+...+4008
2005+2(1+2+3+..+2004)=
2005+2*(2004*2005)/2=   2 cu 2 se simplif
2005+2004*2005=
2005(1+2004)=
2005*2005  NU are rost sa faci calculele pt ca rez e un numar mult prea mare

1996+2+4+...+3990
1996+2 (1+2+3+...+1995)=
1996+2*(1995*1996)/2    2 cu 2 se simplifica iar
1996+1995*1996=
1996(1+1995)=
1996*1996

Answer 2

S1= 2005 + 2(1+2+3+....+2004)=

=2005 +2 * (1+2004)*2004/2

=2005 + (1+2004)*2004)

=2005+2005*2004

=2005(1+1*2004)

=2005*2005

=2005²

S2=1996+2(1+2+3+....+1995)=

=1996+2* (1+1995)*1995/2

=1996+(1+1995)*1995

=1996+1996*1995

=1996(1+1*1995)

=1996*1996

=1996²