Question

CMR:

\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{100}}>10\)

Answer 1

Cái này trong violympic toán có nek! 

Answer 2

Ta có : \(\frac{1}{\sqrt{1}}>\frac{1}{\sqrt{100}}\) ; \(\frac{1}{\sqrt{2}}>\frac{1}{\sqrt{100}}\) ; ....;\(\frac{1}{\sqrt{99}}>\frac{1}{\sqrt{100}};\frac{1}{\sqrt{100}}\) = \(\frac{1}{\sqrt{100}}\)

=> \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}>\frac{1}{\sqrt{100}}+\frac{1}{\sqrt{100}}+...+\frac{1}{\sqrt{100}}\) ( có 100 số \(\frac{1}{\sqrt{100}}\) )

=>\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}>\frac{100}{10}=10\)