1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 < 7/14

1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 <1/14 +1/14 +1/14 +1/14 +1/14 +1/14 +1/14 

dù 1/3>1/14 nhưng :1/30<1/14 1/32<1/14 ;1/35<1/14 ;1/45<1/14 ;1/47<1/14 ;1/50<1/14 

nên: 1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 < 1/2

Ta có: \(\frac{1}{32}< \frac{1}{30};\frac{1}{35}< \frac{1}{30}\)

=> \(\frac{1}{30}+\frac{1}{32}+\frac{1}{35}< \frac{1}{30}+\frac{1}{30}+\frac{1}{30}=\frac{1}{10}\)

\(\frac{1}{47}< \frac{1}{45};\frac{1}{50}< \frac{1}{45}\)

=> \(\frac{1}{45}+\frac{1}{47}+\frac{1}{50}< \frac{1}{45}+\frac{1}{45}+\frac{1}{45}=\frac{3}{45}=\frac{1}{15}\)

=> \(\frac{1}{3}+\frac{1}{30}+\frac{1}{32}+\frac{1}{35}+\frac{1}{45}+\frac{1}{50}< \frac{1}{3}+\frac{1}{10}+\frac{1}{15}=\frac{1}{2}\)

Ta có : 1/3 < 1/2
1/30 < 1/2
1/32 < 1/2
1/35 < 1/2
1/45 < 1/2
1/47 < 1/2
1/50 < 1/2
=> 1/3 + 1/30 + 1/32 + 1/35 + 1/45 + 1/47 + 1/50 < 1/2
@Ác Quỷ Bóng Tối

\(\dfrac{1}{3}+\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{35}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{50}< \dfrac{1}{2}\)

\(\Rightarrow\)\(\dfrac{1}{3}+\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{35}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{50}< \dfrac{7}{14}\)

\(\Rightarrow\dfrac{1}{3}+\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{35}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{50}< \dfrac{1}{14}+\dfrac{1}{14}+\dfrac{1}{14}+\dfrac{1}{14}+\dfrac{1}{14}+\dfrac{1}{14}+\dfrac{1}{14}\)

Dù \(\dfrac{1}{3}>\dfrac{1}{14}\) nhưng:

\(\dfrac{1}{30}< \dfrac{1}{14}\)

\(\dfrac{1}{32}< \dfrac{1}{14}\)

\(\dfrac{1}{35}< \dfrac{1}{14}\)

\(\dfrac{1}{45}< \dfrac{1}{14}\)

\(\dfrac{1}{47}< \dfrac{1}{14}\)

\(\dfrac{1}{50}< \dfrac{1}{14}\)

\(\Rightarrow\) \(\dfrac{1}{3}+\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{35}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{50}< \dfrac{1}{2}\)

Ta có : 1/2>1/3

            1/2>1/30

            1/2>1/32

            1/2>1/35

             1/2>1/45

             1/2>1/47

             1/2>1/50

=>(1/3+1/30+1/32+1/35+1/45+1/47+1/50)<(1/2+1/2+1/2+1/2+1/2+1/2+1/2)

=>(1/3+1/30+1/32+1/35+1/45+1/47+1/50)<1/2

=> 0.4614154846 < 0.5

1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 < 7/14

1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 <1/14 +1/14 +1/14 +1/14 +1/14 +1/14 +1/14 

dù 1/3>1/14 nhưng :1/30<1/14 1/32<1/14 ;1/35<1/14 ;1/45<1/14 ;1/47<1/14 ;1/50<1/14 

nên: 1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 < 1/2

1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 < 7/14

1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 <1/14 +1/14 +1/14 +1/14 +1/14 +1/14 +1/14 

dù 1/3>1/14 nhưng :1/30<1/14 1/32<1/14 ;1/35<1/14 ;1/45<1/14 ;1/47<1/14 ;1/50<1/14 

nên: 1/3+1/30+1/32+1/35+1/45 +1/47 +1/50 < 1/2

vì nếu 2 số có chung một tử số thì số nào có mẫu số lớn hơn thì số đó lớn hơn

s<2/3