Question

chứng minh S = 1/11 + 1/12 + ... + 1/19 + 1/20>1/2

Answer 1

Ta có:\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+.........+\frac{1}{19}+\frac{1}{20}\)

\(>\frac{1}{20}+\frac{1}{20}+........+\frac{1}{20}\)     (có 10 số \(\frac{1}{20}\))

\(=\frac{1}{20}.10=\frac{1}{2}\)

\(\Rightarrow S>\frac{1}{2}\left(đpcm\right)\)

Answer 2

Ta có : 1/11 < 1/20 , 1/12 < 1/20 , .. , 1/19 < 1/20 , 1/20 = 1/20

=> 1/11 + 1/12 + ...+ 1/19 + 1/20 > 1/20 . 10 

=>               S > 10/20

=>               S > 1/2 

Chúc học giỏi !!! ^_^ 

Answer 3

We have S = 1/11 + 1/12 + 1/13 + ... + 1/19 + 1/20 so S has 10 terms 
And 1/2 = 10/20 = 
1/11> 1/12 > 1/13> 1/14> 1/15> 1/16> 1/17> 1/18> 1/19> 1/20 1/11 + 1/12
+ 1/13  + ... + 1 / 19 + 1/20> 1 / 20x10
=> 1/11 + 1/12 + 1/13 + ... + 1/19 + 1/20> 10/20
=> 1/11 +  1/12  + 1 / 
S + / + S + 1/2

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