Question

•Identificand un factor comun,in fiecare suma,calculati:

b) 10+20+30+.......+1230=.......
c) 7+14+21+......+315=

Answer 1

b) 10+20+30+.......+1230=.......
dam factor comun pe 10
10(1+2+3+...+123)

1+2+3+....+n are formula n (n+1)/2
In cazul nostru n=123
deci 1+2+3+....+123=123*124/2=
123*62=7626
10*7626=76260

c) 7+14+21+......+315= dsam factor comun pe 7
7(1+2+3+...+45)

Folosim aceeasi formula pentru suma=
45*46/2=
45*23=1035
7*1035=7245

Answer 2

10(1+2+3+.....123)=10x123x124:2=76260
7x(1+2+3+....45)=7x45x46:2=7245