Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Ta có: 20082 > 20082 -1 = 2007.2009 => 1007/1008<1008/1009
Ta có:\(\frac{1007}{1008}=1-\frac{1}{1008}\)
\(\frac{1008}{1009}=1-\frac{1}{1009}\)
mà \(\frac{1}{1008}>\frac{1}{1009}\)
=> \(1-\frac{1}{1008}< 1-\frac{1}{1009}\)
Hay \(\frac{1007}{1008}< \frac{1008}{1009}\)
Vậy .......
Chúc bạn hk tốt!!! nhớ k cho mình na
\(\dfrac{4}{7}v\text{à }\dfrac{16}{63}\\ \dfrac{4}{7}=\dfrac{4\cdot9}{7\cdot9}=\dfrac{36}{63}\\ \dfrac{36}{63}>\dfrac{16}{63}\\ \Rightarrow\dfrac{4}{7}>\dfrac{16}{36}\)
\(\dfrac{4}{17}\) và \(\dfrac{16}{63}\)
\(\dfrac{4}{63}>\dfrac{16}{63}\)
\(=>\dfrac{4}{17}>\dfrac{16}{63}\)
\(\dfrac{5}{29}\) và \(\dfrac{7}{33}\)
\(\dfrac{5}{33}< \dfrac{7}{33}\)
\(=>\dfrac{5}{29}< \dfrac{7}{33}\)
\(\dfrac{44}{57}\) và \(\dfrac{89}{99}\)
\(\dfrac{44}{99}< \dfrac{89}{99}\)
\(=>\dfrac{44}{57}< \dfrac{89}{99}\)
\(\dfrac{19}{53}\) và \(\dfrac{30}{73}\)
\(\dfrac{19}{73}>\dfrac{30}{73}\)
\(=>\dfrac{19}{53}>\dfrac{30}{73}\)
\(1-\frac{1003}{1005}=\frac{2}{1005}>\frac{2}{1007}=1-\frac{1005}{1007}\Rightarrow\frac{1003}{1005}
ta có : 1-1003/1005=2/1005
1-1005/1007=2/1007
vì 2/1005>2/1007 nên 1003/1005<1005/1007
Đặt \(A=\frac{1005}{1006}+\frac{1006}{1007}+\frac{1007}{1008}+\frac{1008}{1005}\) ta có :
\(A=\frac{1006-1}{1006}+\frac{1007-1}{1007}+\frac{1008-1}{1008}+\frac{1005+3}{1005}\)
\(A=\frac{1006}{1006}-\frac{1}{1006}+\frac{1007}{1007}-\frac{1}{1007}+\frac{1008}{1008}-\frac{1}{1008}+\frac{1005}{1005}+\frac{3}{1005}\)
\(A=1-\frac{1}{1006}+1-\frac{1}{1007}+1-\frac{1}{1008}+1+\frac{3}{1005}\)
\(A=\left(1+1+1+1\right)-\left(\frac{1}{1006}+\frac{1}{1007}+\frac{1}{1008}-\frac{3}{1005}\right)\)
\(A=4-\left(\frac{1}{1006}+\frac{1}{1007}+\frac{1}{1008}-\frac{1}{1005}-\frac{1}{1005}-\frac{1}{1005}\right)\)
\(A=4-\left[\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)\right]\)
Mà :
\(\frac{1}{1006}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1006}-\frac{1}{1005}< 0\) \(\left(1\right)\)
\(\frac{1}{1007}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1007}-\frac{1}{1005}< 0\) \(\left(2\right)\)
\(\frac{1}{1008}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1008}-\frac{1}{1005}< 0\) \(\left(3\right)\)
Từ (1), (2) và (3) suy ra :
\(\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)< 0\)
\(\Rightarrow\)\(A=4-\left[\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)\right]>4\)
\(\Rightarrow\)\(A>4\) ( điều phải chứng minh )
Vậy \(A>4\)
Chúc bạn học tốt ~
\(\dfrac{4}{17}=\dfrac{16}{68}\\ Vì:\dfrac{16}{68}< \dfrac{16}{63}\Rightarrow\dfrac{4}{17}< \dfrac{16}{63}\\ ---\\ \dfrac{1007}{1009}=1-\dfrac{2}{1009};\dfrac{1005}{1007}=1-\dfrac{2}{1007}\\ Vì:\dfrac{2}{1009}< \dfrac{2}{1007}\Rightarrow1-\dfrac{2}{1009}>1-\dfrac{2}{1007}\\ \Rightarrow\dfrac{1007}{1009}>\dfrac{1005}{1007}\)
a: 4/17=16/68
16/68<16/63
=>4/17<16/63
b: 19/53<20/53
20/53<20/50(Vì 53>50)
=>19/53<20/50=2/5
mà 2/5=30/75<30/73
nên 19/53<30/73
c: 1007/1009=1-2/1009
1005/1007=1-2/1007
1009>1007
=>2/1009<2/1007
=>-2/1009>-2/1007
=>1007/1009>1005/1007