Oblicz
: 29 mar 2018, 23:37
Oblicz wartość wyrażenia\(\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+...+\frac{1}{\sqrt{2017}+\sqrt{2019}}\).
\(\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+...+\frac{1}{\sqrt{2017}+\sqrt{2019}}=
\frac{ \sqrt{3}-1 }{2}+ \frac{ \sqrt{5}- \sqrt{3} }{2}+ \frac{ \sqrt{7}- \sqrt{5} }{2}+...+ \frac{ \sqrt{2019}- \sqrt{2017} }{2}= \frac{ \sqrt{2019}- 1 }{2}\)