Question

rezolvați ecuațiile b) (x-1)+(x-2)+(x-3)+....(x-20)=0 c) x-2x+3x-4x+....+99x-100x=500 d) x/1*2+x/2*3+x/3*4+.....+x/199*200=398​

Answer 1

b) (x-1)+(x-2)+(x-3)+....(x-20)=
=20x-1-2-3-...-20=
=20x-(1+2+3+...+20)=
=20x-20*21/2=
=20x-210
Deci 20x-210=0
20x=210
x=210/20
x=10,5

c) x-2x+3x-4x+...+99x-100x=
=x(1-2+3-4+...+99-100)=
=x[(1-2)+(3-4)+...+(99-100)]=
=-50x
Deci -50x=500
x=-500/50
x=-10

d) x/1*2+x/2*3+x/3*4+...+x/199*200=
=x(1/1*2+1/2*3+1/3*4+...+1/199*200)=
=x(1/1-1/2+1/2-1/3+1/3-1/4+...+1/199-1/200)=
=x(1-1/200)=
=x*199/200
Deci x*199/200=398
x=398*200/199
x=400