Question

CUM SE REZOLVA EXERCITIUL (3+6+9+...+30)-(2+4+6+...+20)

Answer 1

facem Gauss pentru fiecare in parte

3(1+2+...+10)=
3*10*11/2=  simplificam 10 cu 2
3*5*11

2+4+6+...+20=
2(1+2+3+...+10)=
2*10*11/2 =   simplificam 2 cu 2
10*11

vom avea
3*5*11-10*11=
11(3*5-10)=
11*(15-10)=
11*5=
55

Answer 2

3+6+9+..........+30=3x(1+2+3+........+10)=3x10x(10+1):2=3x10x11:2=165
2+4+6+........+20=2x(1+2+3+.......+10)=2x10x(10+1):2=2x10x11:2=110
165-110=55
sau o rezolvare mai scurta
(3+6+9+...........+30)-(2+4+6+.........+20)=1+2+3+........+10=10x(10+1):2=10x11:2= 55