Question

[Bẩy Bẩy]

ai giúp mik với CMR:

1/10+1/11+1/12+...+1/199+1/200>3/2

Answer 1

[Ngoc Anh Thai]

\(A=\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}+...+\dfrac{1}{199}+\dfrac{1}{200}\\ >\dfrac{1}{10}+\left(\dfrac{1}{100}+\dfrac{1}{100}+...+\dfrac{1}{100}\right)\left(90so\right)+\left(\dfrac{1}{200}+\dfrac{1}{200}+...+\dfrac{1}{200}\right)\left(100so\right)\\ A>\dfrac{1}{10}+\dfrac{90}{100}+\dfrac{100}{200}=1+\dfrac{1}{2}=\dfrac{3}{2}\left(đpcm\right).\)