Question 44
The positive real numbers $a$, $b$, $c$ satisfy the equality $a + b + c = 1$. For every natural number $n$ find the minimal possible value of the expression
$$
E = \frac{a^{-n} + b}{1 - a} + \frac{b^{-n} + c}{1 - b} + \frac{c^{-n} + a}{1 - c}
$$
$$
E = \frac{a^{-n} + b}{1 - a} + \frac{b^{-n} + c}{1 - b} + \frac{c^{-n} + a}{1 - c}
$$