Question

Rezolvati :
1) 1+3+5+7+9+...+19

2)5+10+15+...+625

Answer 1

1) 1+3+5+7+...+19=
=(2*0+1)+(2*1+1)+(2*2+1)+...+(2*9+1)=
=2(0+1+2+3+..+9)+1+1+1...+1 (de 10 ori)=
=2*9*10/2+10=
=9*10+10=
=10(9+1)=
=10*10=
=100

2)5+10+15+...+625=
=5(1+2+3+..+125)=
=5*125*126/2=
=5*125*63=
=39375

Answer 2

1+3+5+7+9+...+19=
=(2*1-1)+(2*2-1)+(2*3-1)+...+(2*10-1)
=10²
=100
5+10+15+...+625=
=5(1+2+3+...+125)
=5*125*126:2
=625*126:2
=78750:2
=39375