Cho tam giác ABC nhọn có đường cao BD, CE . trên BD, CE lấy điểm M, N sao cho \(\widehat{BNA}=\widehat{CMA}=90^O\) . CMR  : \(\widehat{AME}=\widehat{AND}\)

Cho a, b > 0 . CMR :

\(\dfrac{a}{b+c}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< \sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}\)

CMR : A > 1,99 với :

A= \(\dfrac{1}{\sqrt{1\cdot199}}+\dfrac{1}{\sqrt{2\cdot189}}+...+\dfrac{1}{\sqrt{199\cdot1}}\)

Cho x, y > 0 và \(\dfrac{x}{2}+\dfrac{8}{y}\le2\) .

Tìm Min A = \(\dfrac{x}{y}+\dfrac{2y}{x}\) 

5.5 kg

CMR : A > 1,99 với :

A= \(\dfrac{1}{\sqrt{1\cdot199}}+\dfrac{1}{2\cdot198}+...+\dfrac{1}{\sqrt{199\cdot1}}\)

CMR :

\(\dfrac{1}{3\left(1+\sqrt{2}\right)}+\dfrac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+\dfrac{1}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\dfrac{1}{4037\left(\sqrt{2018}+\sqrt{2019}\right)}< \dfrac{1}{2}\)