Question

o resultado da expressão numérica:
$0.333... + \frac{ { (\frac{1}{2} + 1) }^{ - 2} }{ {( - 2 - 1)}^{2} }$
é igual a :
a)1
b)2
c)4
d)5
e) n.r.a.

Answer 1

$0,333...+\frac{(\frac{1}{2}+1)^{-2}}{(-2-1)^2}=\\\\ =\frac{1}{3}+\frac{(\frac{1+2}{2})^{-2}}{(-3)^2}=\\\\ =\frac{1}{3}+\frac{(\frac{3}{2})^{-2}}{(-3)^2}=\\\\ =\frac{1}{3}+\frac{(\frac{2}{3})^{2}}{(9)}=\\\\ =\frac{1}{3}+\frac{\frac{4}{9}}{9}=\\\\ =\frac{1}{3}+\frac{4}{9}.\frac{1}{9}=\\\\ =\frac{1}{3}+\frac{4}{81}=\\\\ =\frac{27+4}{81}=\\\\ =\frac{31}{81}$