Întrebare problema cu radicali

Aratati ca:

Buna seara,

$\sqrt{2+\sqrt{2}}<\sqrt{2+2}=\sqrt{4}=2$,
$\sqrt{6+\sqrt{6}}<\sqrt{6+3}=\sqrt{9}=3$,
$\sqrt{12+\sqrt{12}}<\sqrt{12+4}=\sqrt{16}=4$,
..........................................................
$\sqrt{210+\sqrt{210}}<\sqrt{210+15}=\sqrt{225}=15$.

Atunci $\sqrt{2+\sqrt{2}}+\sqrt{6+\sqrt{6}}+\sqrt{12+\sqrt{12}}+...+\sqrt{210+\sqrt{210}}<$

$<2+3+4+...+15=119$.