Question

Suma lui gaus
1) 1+2+3+.........…+50=
2) 2+4+6+8+.….......+80=

Answer 1

1)  1+2+3+...+50=
  = 50x(50+1):2=
   =50x51:2=
    =25x51=1275
2) 2+4+6+...+80=
    =2x1+2x2+2x3+...+2x40=
    =2x(1+2+3+...+40)=
     =2x40x41:2=
      =80x41:2=
       =40x41=1640

Answer 2

$\displaystyle a).1+2+3+...+50= \frac{50(50+1)}{2} = \frac{50 \times 51}{2} = \frac{2550}{2} =1275 \\ \\ b).2+4+6+8+...+80=2(1+2+3+...+40)=2 \times \frac{40(40+1)}{2} = \\ \\ =2 \times \frac{40 \times 41}{2} =\not 2 \times \frac{1640}{\not 2} =1640$