Question

Вычислите сумму)))))))) ​

Answer 1

$\frac{1}{\sqrt{3}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{11}}+\frac{1}{\sqrt{11}+\sqrt{15}}+...+\frac{1}{\sqrt{27}+\sqrt{31}}\\\\-\frac{\sqrt{3}-\sqrt{7}}{4}-\frac{\sqrt{7}-\sqrt{11}}{4}-\frac{\sqrt{11}-\sqrt{15}}{4}-...-\frac{\sqrt{27}-\sqrt{31}}{4}\\-\frac{\sqrt{3}}{4}+\frac{\sqrt{7}}{4}-\frac{\sqrt{7}}{4}+\frac{\sqrt{11}}{4}-\frac{\sqrt{11}}{4}+\frac{\sqrt{15}}{4}-...-\frac{\sqrt{27}}{4}+\frac{\sqrt{31}}{4}\\-\frac{\sqrt{3}}{4}+\frac{\sqrt{31}}{4}=\frac{\sqrt{31}-\sqrt{3}}{4}$