

Chứng minh rằng [tex]S=\frac{1}{3(1+\sqrt{2})}+\frac{1}{5(\sqrt{2}+\sqrt{3})}+\frac{1}{7(\sqrt{3}+\sqrt{4})}+...+\frac{1}{97(\sqrt{48}+\sqrt{49})}< \frac{3}{7}[/tex]
p/s: em biết tính [tex]\frac{1}{(1+\sqrt{2})}+\frac{1}{(\sqrt{2}+\sqrt{3})}+\frac{1}{(\sqrt{3}+\sqrt{4})}+...+\frac{1}{(\sqrt{48}+\sqrt{49})} = \sqrt{49}-1 = 6[/tex] rồi ạ
p/s: em biết tính [tex]\frac{1}{(1+\sqrt{2})}+\frac{1}{(\sqrt{2}+\sqrt{3})}+\frac{1}{(\sqrt{3}+\sqrt{4})}+...+\frac{1}{(\sqrt{48}+\sqrt{49})} = \sqrt{49}-1 = 6[/tex] rồi ạ