`P=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}`
`=\frac{\sqrt{1}-\sqrt{2}}{(\sqrt{1}-\sqrt{2})(\sqrt{1}+\sqrt{2})}+\frac{\sqrt{2}-\sqrt{3}}{(\sqrt{2}-\sqrt{3})(\sqrt{2}+\sqrt{3})}+...+\frac{\sqrt{99}-\sqrt{100}}{(\sqrt{99}+\sqrt{100})(\sqrt{99}-\sqrt{100})}`
`=\frac{\sqrt{1}-\sqrt{2}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+....+\frac{\sqrt{99}-\sqrt{100}}{99-100}`
`=\frac{\sqrt{1}-\sqrt{2}}{-1}+\frac{\sqrt{2}-\sqrt{3}}{-1}+...+\frac{\sqrt{99}-\sqrt{100}}{-1}`
`=\frac{\sqrt{1}-\sqrt{2}+\sqrt{2}-\sqrt{3}+\sqrt{3}-.....-\sqrt{99}+\sqrt{99}-\sqrt{100}}{-1}`
`=\frac{\sqrt{1}-\sqrt{100}}{-1}`
`=\frac{\sqrt{1^2}-\sqrt{10^2}}{-1}`
`=\frac{1-10}{-1}`
`=\frac{-9}{-1}`
`=9`
Cách giải: Nhân lượng liên hợp `->` Rút gọn `->` Kết quả.
