Question

1/1+√2+1/√2+√3+..........+1/√99+√100=?

Answer 1

Hello,

$\dfrac{1}{\sqrt{1}+\sqrt{2}} +\dfrac{1}{\sqrt{2}+\sqrt{3}} +....+\dfrac{1}{\sqrt{98}+\sqrt{99}} +\dfrac{1}{\sqrt{99}+\sqrt{100}} \\\\ =\dfrac{\sqrt{2}-\sqrt{1}}{2-1}+\dfrac{\sqrt{3}-\sqrt{2}}{3-2}+\dfrac{\sqrt{4}-\sqrt{3}}{4-3}+...+\dfrac{\sqrt{99}-\sqrt{98}}{99-98}+\dfrac{\sqrt{100}-\sqrt{99}}{100-99}\\ =-\sqrt{1}+\sqrt{100}\\ =10-1\\ =9$