Question

Sã se rezolve ecuația: x+(x+4)+(x+2•4)+...+(x+100•4)=(200+100•4)•101 totul supra 2.

Answer 1

x+(x+4)+(x+2•4)+...+(x+100•4)=(200+100•4)•101/2

(x+x+...de 101 ori...+x)+(0*4+1*4+2*4+3*4+...+100*4)=600*101/2

101x+4(1+2+3+...+100)=300*101

101x+4(100*101)/2=300*101

101x+200*101=300*101, impartim prin 101:

x+200=300

x=100

Dupa ce am dat factor comun pe 4, am folosit formula: 1+2+3+...+n=n(n+1)/2