Question

Calculați: 1) 2+4+6+8+...+2010=
2) 5+10+15+20+...+2010=
Repede va rog frumos

Answer 1

1) 2+4+6+8+...+2010=2·1+2·2+2·3+2·4+...+2·1005=

=2(1+2+3+4+...+1005)=

=2(1005·1006/2)=

=1005·1006=

=1011030

2)

5+10+15+20+...+2010=

=5·1+5·2+5·3+5·4+...+5·402=

=5(1+2+3+4+...+402)=

=5(402·403/2)=

=5·201·403=

=1005·403=

=405015