Question

2.)Identificind  un factor comun, in fiecare suma , calculati:

3+6+9+.....+66

10+20+30+......+1230

7+14+21+.....315

 

Answer 1

3(1+2+...+22)=3(23*22):2=3(23*11)=759


10(1+2+...+123)=10(123*124):2=10(123*62)=76260


7(1+2+...+45)=7(45*46):2=7(45*23)=7245

Answer 2

1) 3+6+9+...+66=3(1+2+3+....22)=

=3(1+22)*22/2

=3*11*23=

=33*23=759

2) 10+20+30+...+1230=10(1+2+3+....+123)=

=10*(1+123)*123/2=

=5*124*123=

=76 260

3)7+14+21+....+315=7(1+2+3+....+45)=

=7(1+45)*45/2=

=7*46*45/2=

=7*23*45=

=7245