Question

Calculati: a) 3+6+9+12+...+2019 b) 4+8+12+...+2020 c)5+10+15+20+...+2020 d)7+14+21+...+2023 prin metoda gauss

Answer 1

a) 3x(1+2+3+4+............+673)=
    3x[673x(673+1):2]=
    3x[673x674:2]=
    3x(453.602:2)=
    3x226.801=680.403
b) 4x(1+2+3+.................+505)=
    4x[505x(505+1):2]=
    4x[505x506:2]=
    4x(255.5330:2)=
    4x127.765=511.060
c) 5x(1+2+3+4+..............+404)=
    5x[404x(404+1):2]=
    5x[404x405:2]=
    5x(163.620:2)=
    5x81.810=409.050
d) 7x(1+2+3+...................+289)=
    7x[289x(289+1):2]=
    7x[289x290:2]=
    7x(83.810:2)=
    7x41.905=293.335