Question

help

Answer 1

\(\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+...+\frac{1}{\sqrt{99}+\sqrt{98}}+\frac{1}{\sqrt{100}+\sqrt{99}}\)

\(=\frac{\sqrt{2}-1}{2-1}+\frac{\sqrt{3}-\sqrt{2}}{3-2}+\frac{\sqrt{4}-\sqrt{3}}{4-3}+...+\frac{\sqrt{99}-\sqrt{98}}{99-98}+\frac{\sqrt{100}-\sqrt{99}}{100-99}\)

\(=\sqrt{2}-1+\sqrt{3}-\sqrt{2}+\sqrt{4}+\sqrt{3}+...+\sqrt{99}-\sqrt{98}+\sqrt{100}-\sqrt{99}\)

\(=\sqrt{100}-1=10-1=9\)

Answer 2

CACL bằng máy tính nhanh hơn đó ay :3