Question

Se considera expresia E(x)=(2x-3)^2-3(x-1)(x+1)-5(2-3x), unde x este numar real. Demonstreaza ca suma 1/E(0)+1/E(1)+…+1/E(8)+0,1 este numar natural.

Answer 1

Răspuns:

Explicație pas cu pas:

E(x) = 4x^2 -12x +9 -3x^2 +3 -10+15x =

  x^2 +3x +2 = (x+1)(x+2)

1/((x+1)(x+2)) = 1/(x+1) -1/(x+2)

S = 1/(1*2)+1/(2*3)+1/(3*4)+...+1/(9*10)+ 1/10 =

1 -1/2 +1/2 -1/3 +1/3 -1/4 +...+1/9 -1/10 +1/10 = 1