Cho A=50/111+50/112+50/113+50/114.Chứng tỏ 1<A<2
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TD
1
16 tháng 5 2017
50/111 < 50/100
50/112 < 50/100
50/113 < 50/100
50/114 < 50/100
=> A < 200/100 => A < 2
50/111 > 50/200
50/112 > 50/200
50/113 > 50/200
50/114 > 50/200
=> A > 200/200 => A > 1
Vậy 1 < A < 2
AI THẤY OK ỦNG HỘ NHÉ
HN
0
NM
2
13 tháng 5 2018
\(\frac{50}{111}>\frac{1}{4};\frac{50}{112}>\frac{1}{4};\frac{50}{113}>\frac{1}{4};\frac{50}{114}>\frac{1}{4}\)
\(A=\frac{50}{111}+\frac{50}{112}+\frac{50}{113}+\frac{50}{114}>\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=1\)(1)
\(\frac{50}{111}< \frac{1}{2};\frac{50}{112}< \frac{1}{2};\frac{50}{113}< \frac{1}{2};\frac{50}{114}< \frac{1}{2}\)
\(\Rightarrow A=\frac{50}{111}+\frac{50}{112}+\frac{50}{113}+\frac{50}{114}< \frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=2\)(2)
từ (1) và (2) \(\Rightarrow1< A< 2\)
KN
15 tháng 4 2019
Ta có :
\(\frac{50}{111}>\frac{50}{200}\)
\(\frac{50}{112}>\frac{50}{200}\)
\(\frac{50}{113}>\frac{50}{200}\)
\(\frac{50}{114}>\frac{50}{200}\)
\(\Rightarrow A>\frac{50}{200}+\frac{50}{200}+\frac{50}{200}+\frac{50}{200}\)hay \(A>\frac{50}{200}.4\left(1\right)\)
Mặt khác :
\(\frac{50}{111}< \frac{50}{100}\)
\(\frac{50}{112}< \frac{50}{100}\)
\(\frac{50}{113}< \frac{50}{100}\)
\(\frac{50}{114}< \frac{50}{100}\)
\(\Rightarrow A< \frac{50}{100}+\frac{50}{100}+\frac{50}{100}+\frac{50}{100}\)hay \(A< \frac{50}{100}.4\left(2\right)\)
Từ \(\left(1\right)\)và \(\left(2\right)\Rightarrow1< A< 2\left(đpcm\right)\)
13 tháng 5 2018
A<50/100+50/100+50/100+50/100=4.50/100=2
=>A<2
A>4.50/150=4/3+1+1/3>1
=>dccm
Ta có :
\(A=\dfrac{50}{111}+\dfrac{50}{112}+\dfrac{50}{113}+\dfrac{50}{114}\)
Ta thấy :
\(\dfrac{50}{111}>\dfrac{50}{200}\)
\(\dfrac{50}{112}>\dfrac{50}{200}\)
\(\dfrac{50}{113}>\dfrac{50}{200}\)
\(\dfrac{50}{114}>\dfrac{50}{200}\)
\(\Rightarrow A>\dfrac{50}{200}+\dfrac{50}{200}+\dfrac{50}{200}+\dfrac{50}{200}\)
\(\Rightarrow A>\dfrac{50}{200}.4=1\) \(\left(1\right)\)
Mặt khác :
\(\dfrac{50}{111}< \dfrac{50}{100}\)
\(\dfrac{50}{112}< \dfrac{50}{100}\)
\(\dfrac{50}{113}< \dfrac{50}{100}\)
\(\dfrac{50}{114}< \dfrac{50}{100}\)
\(\Rightarrow A< \dfrac{50}{100}+\dfrac{50}{100}+\dfrac{50}{100}+\dfrac{50}{100}\)
\(\Rightarrow A< \dfrac{50}{100}.4=2\) \(\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Rightarrow1< A< 2\rightarrowđpcm\)