Toán 6 Thi hk2

[Hồng Uyên 2k6]

[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
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Chứng minh rằng :
S=[tex]\frac{1}{31}+\frac{1}{32}+\frac{1}{3}+....+\frac{1}{60}<\frac{4}{5}[/tex]

 

[Blue Plus]

Chứng minh rằng :
S=[tex]\frac{1}{31}+\frac{1}{32}+\frac{1}{3}+....+\frac{1}{60}<\frac{4}{5}[/tex]

$ \dfrac{1}{31} < \dfrac{1}{30}\\\dfrac{1}{32} < \dfrac{1}{30}\\\dfrac{1}{33} < \dfrac{1}{30}\\...\\\dfrac{1}{40} < \dfrac{1}{30}\\\Rightarrow \dfrac{1}{31} + \dfrac{1}{32} + \dfrac{1}{33} + ... + \dfrac{1}{40} < 10 . \dfrac{1}{30} = \dfrac{1}{3} $
$ \dfrac{1}{41} < \dfrac{1}{40}\\\dfrac{1}{42} < \dfrac{1}{40}\\\dfrac{1}{43} < \dfrac{1}{40}\\...\\\dfrac{1}{50} < \dfrac{1}{40}\\\Rightarrow \dfrac{1}{41} + \dfrac{1}{42} + \dfrac{1}{43} + ... + \dfrac{1}{50} < 10 . \dfrac{1}{40} = \dfrac{1}{4} $
$ \dfrac{1}{51} < \dfrac{1}{50}\\\dfrac{1}{52} < \dfrac{1}{50}\\\dfrac{1}{53} < \dfrac{1}{50}\\...\\\dfrac{1}{60} < \dfrac{1}{50}\\\Rightarrow \dfrac{1}{51} + \dfrac{1}{52} + \dfrac{1}{53} + ... + \dfrac{1}{60} < 10 . \dfrac{1}{50} = \dfrac{1}{5} $
$ \Rightarrow S < \dfrac13 + \dfrac14 + \dfrac15 = \dfrac{47}{60} < \dfrac{48}{60} = \dfrac{4}{5} $

 

[Hồng Uyên 2k6]

$ \dfrac{1}{31} < \dfrac{1}{30}\\\dfrac{1}{32} < \dfrac{1}{30}\\\dfrac{1}{33} < \dfrac{1}{30}\\...\\\dfrac{1}{40} < \dfrac{1}{30}\\\Rightarrow \dfrac{1}{31} + \dfrac{1}{32} + \dfrac{1}{33} + ... + \dfrac{1}{40} < 10 . \dfrac{1}{30} = \dfrac{1}{3} $
$ \dfrac{1}{41} < \dfrac{1}{40}\\\dfrac{1}{42} < \dfrac{1}{40}\\\dfrac{1}{43} < \dfrac{1}{40}\\...\\\dfrac{1}{50} < \dfrac{1}{40}\\\Rightarrow \dfrac{1}{41} + \dfrac{1}{42} + \dfrac{1}{43} + ... + \dfrac{1}{50} < 10 . \dfrac{1}{40} = \dfrac{1}{4} $
$ \dfrac{1}{51} < \dfrac{1}{50}\\\dfrac{1}{52} < \dfrac{1}{50}\\\dfrac{1}{53} < \dfrac{1}{50}\\...\\\dfrac{1}{60} < \dfrac{1}{50}\\\Rightarrow \dfrac{1}{51} + \dfrac{1}{52} + \dfrac{1}{53} + ... + \dfrac{1}{60} < 10 . \dfrac{1}{50} = \dfrac{1}{5} $
$ \Rightarrow S < \dfrac13 + \dfrac14 + \dfrac15 = \dfrac{47}{60} < \dfrac{48}{60} = \dfrac{4}{5} $

thank chị

 

[Dương Sảng]

S = ( 1/31 + 1/32 + ...... + 1/ 40 ) + ( 1/41 + 1/42 + ...... + 1/50 ) + ( 1/51 + 1/52 + ...... + 1/60 )
Vì S < ( 1/30 + 1/30 + ...... + 1/30 ) + ( 1/40 + 1/40 + ...... + 1/40 ) + ( 1/50 + 1/50 + ...... + 1/50 )
=> S < 10.1/30 + 10.1/40 + 10.1/50 = 47/60 < 48/60 = 4/5
=> S < 4/5