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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 : 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:
\(\dfrac{1}{30}< \dfrac{1}{14}\)
\(\dfrac{1}{32}< \dfrac{1}{14}\)
\(\dfrac{1}{35}< \dfrac{1}{14}\)
\(\dfrac{1}{45}< \dfrac{1}{14}\)
\(\dfrac{1}{47}< \dfrac{1}{14}\)
\(\dfrac{1}{50}< \dfrac{1}{14}\)
\(\Rightarrow\) \(\dfrac{1}{3}+\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{35}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{50}< \dfrac{1}{2}\)
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
Ta có: Gọi dãy số cần chứng minh là A
A<(130 +130 +130 )+(160 +160 +160 +160 )
A<13 +330 +460
A<1030 +330 +230
A<1330 +230
A<1530 =12
Vậy A<12
Ta có: \(\frac{1}{32}< \frac{1}{30};\frac{1}{35}< \frac{1}{30}\)
=> \(\frac{1}{30}+\frac{1}{32}+\frac{1}{35}< \frac{1}{30}+\frac{1}{30}+\frac{1}{30}=\frac{1}{10}\)
\(\frac{1}{47}< \frac{1}{45};\frac{1}{50}< \frac{1}{45}\)
=> \(\frac{1}{45}+\frac{1}{47}+\frac{1}{50}< \frac{1}{45}+\frac{1}{45}+\frac{1}{45}=\frac{3}{45}=\frac{1}{15}\)
=> \(\frac{1}{3}+\frac{1}{30}+\frac{1}{32}+\frac{1}{35}+\frac{1}{45}+\frac{1}{50}< \frac{1}{3}+\frac{1}{10}+\frac{1}{15}=\frac{1}{2}\)