Question

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

Answer 1

1/1+1/2+1/3+..........+1/100>1/100+1/100+1/100+.....+1/100(co 100 so)

=>1/1+1/2+1/3+....+1/100>1

mà 1/căn 100=1/10

=>1/căn 100+1/căn 100+.....+1/căn 100=10

=>1/căn 1+1/ căn 2+.....+1/ căn 100>10

sorry mình ko biết gõ căn bậc 2

 

Answer 2

Đặt A = \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+....+\frac{1}{\sqrt{100}}\)

A > \(\frac{1}{\sqrt{100}}+\frac{1}{\sqrt{100}}+\frac{1}{\sqrt{100}}+....+\frac{1}{\sqrt{100}}\)(100 số)

A > \(\frac{1}{\sqrt{100}}.100\)

=> A > 10

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