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Решите задачу:

$\frac{1}{\sqrt1+\sqrt3} + \frac{1}{\sqrt3+\sqrt5} +...+ \frac{1}{\sqrt{119}+\sqrt{121}} =\\\\= \frac{\sqrt1-\sqrt3}{(\sqrt1+\sqrt3)(\sqrt1-\sqrt3)} +\frac{\sqrt3-\sqrt5}{(\sqrt3+\sqrt5)(\sqrt3-\sqrt5)}+...+\frac{\sqrt{119}-\sqrt{121}}{(\sqrt{119}+\sqrt{121})(\sqrt{119}-\sqrt{121})}=\\\\=\frac{\sqrt1-\sqrt3}{1-3}+ \frac{\sqrt3-\sqrt5}{3-5}+...+ \frac{\sqrt{119}-\sqrt{121}}{119-121}=\\\\= \frac{\sqrt1-\sqrt3}{-2} +\frac{\sqrt3-\sqrt5}{-2} +...+ \frac{\sqrt{119}-\sqrt{121}}{-2}=$

$=- \frac{1}{2}\cdot (\sqrt1-\sqrt3+\sqrt3-\sqrt5+\sqrt5-\sqrt7+...+\sqrt{117}-\sqrt{119}+\\\\+\sqrt{119}-\sqrt{121})= - \frac{1}{2}\cdot (\sqrt1-\sqrt{121})=- \frac{1}{2}\cdot (1-11)=\frac{10}{2}=5$