Question

[Thảo Trần]

cho S=6/15 + 6/16 + 6/17 + 6/18 + 6/19

a,CM rằng 1<S<2

b,TỪ câu a suy ra S không thuộc Z

mọi người giúp mình  nha

Answer 1

[Arima Kousei]

a ) CM : S < 1

Ta có : 

6 /15> 6/30                  

6 /16> 6/30 

6/17 > 6/30 

6/18 > 6/30

6/19 > 6 / 30 

=>     S = 6/15 + 6/16 + 6/17 + 6/18 + 6/19 > 6/30 x 5 = 1 

=>     S > 1 ( 1 ) 

CM :           S < 2 

6/16 < 6/15 , 6/17 < 6/15 , 6/18 < 6/15 , 6/19 < 6/15

=>      S = 6/15 + 6/16+ 6/17 + 6/18 + 6/19 < 6/15 x 5 = 2 

=>      S < 2 ( 2 )

Từ ( 1 ) , ( 2 ) =>                1 < S < 2 

b )    Do 1 < S < 2  => S ko phải STN
Chúc học giỏi !!! 

Answer 2

[Dũng Lê Trí]

\(S=\frac{6}{15}+\frac{6}{16}+\frac{6}{17}+\frac{6}{18}+\frac{6}{19}>\frac{6}{20}+\frac{6}{20}+\frac{6}{20}+\frac{6}{20}+\frac{6}{20}\)

\(S>\frac{6}{20}\cdot5=\frac{30}{20}\)

\(\Rightarrow S>\frac{3}{2}>1\)

\(S< \frac{6}{14}+\frac{6}{14}+\frac{6}{14}+\frac{6}{14}+\frac{6}{14}\)

\(S< \frac{6}{14}\cdot5=\frac{30}{14}\)

\(S< \frac{15}{7}\Rightarrow S< \frac{14}{7}+\frac{1}{7}\)

\(S< 2+\frac{1}{7}\)

\(\Rightarrow1< \frac{3}{2}< S< 2< 2+\frac{1}{7}\)

\(\Leftrightarrow1< S< 2\Rightarrow S\notin Z\)