12.3.1.10 Algebraic

Condition: Prove that for arbitrary positive real numbers \ (a_ {1}, a_ {2}, \ ldots, a_ {n} \) inequality is performed: \ [[ \ frac {n} {\ frac {1} {1+a_ {1}}+\ frac {1} {1+a_ {2}}+\ cdots+\ frac {1} {1+a_ {n }}}-\ frac {n} {\ frac {1} {a_ {1}}+\ frac {1} {a_ {2}}+\ cdots+\ frac {1} {a_ {n}}}}}}}}}}} \ geq 1 \]