\(C=\dfrac{1}{\sqrt{2017}+\sqrt{2015}}+\dfrac{1}{\sqrt{2015}+\sqrt{2013}}+...+\dfrac{1}{\sqrt{3}+\sqrt{1}}\)
\(C=\dfrac{\sqrt{2017}-\sqrt{2015}}{\left(\sqrt{2017}+\sqrt{2015}\right)\left(\sqrt{2017}-\sqrt{2015}\right)}+\dfrac{\sqrt{2015}-\sqrt{2013}}{\left(\sqrt{2015}+\sqrt{2013}\right)\left(\sqrt{2015}-\sqrt{2013}\right)}+...+\dfrac{\sqrt{3}-\sqrt{1}}{\left(\sqrt{3}+\sqrt{1}\right)\left(\sqrt{3}-\sqrt{1}\right)}\)
\(C=\dfrac{\sqrt{2017}-\sqrt{2015}}{\left(\sqrt{2017}\right)^2-\left(\sqrt{2015}\right)^2}+\dfrac{\sqrt{2015}-\sqrt{2013}}{\left(\sqrt{2015}\right)^2-\left(\sqrt{2013}\right)^2}+...+\dfrac{\sqrt{3}-\sqrt{1}}{\left(\sqrt{3}\right)^2-\left(\sqrt{1}\right)^2}\)
\(C=\dfrac{\sqrt{2017}-\sqrt{2015}+\sqrt{2015}-\sqrt{2013}+...+\sqrt{3}-\sqrt{1}}{2}\)
\(C=\dfrac{\sqrt{2017}-1}{2}\)
