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 \(\sqrt{2+\sqrt{2}}+\sqrt{6+\sqrt{6}}+\sqrt{12+\sqrt{12}}+...+\sqrt{210+\sqrt{210}}<\)

\(<2+3+4+...+15=119\).