Question

20PCT! Va rog! Poza mai jos.

Answer 1

a)
aplicam relatiile viette pentru numitorii termenilor lui E(x) si observam ca radacinile sunt intregi si fac parte din multimea:
r∈[-2011;0]
prin urmare domeniul de definitie este:
x∈R\r

b)
1/x(x+1)=1/x - 1/(1+x)
1/(x+1)(x+2)=1/(x+1) - 1/(x+2)
1/(x+2)(x+3)=1/(x+2) - 1/(x+3)
..............................................
1/(x+2009)(x+2010)=1/(x+2009) - 1/(x+2010)
1/(x+2010)(x+2011)=1/(x+2010) - 1/(x+2011) le adunam si obtinem:

E(x)=1 - 1/(x+2011)
E(x)=(x+2010)/(x+2011)

c)
2011/E(x)=x+2011
2011=x+2010
x=1