Ta có \(\frac{178}{179}+\frac{179}{180}+\frac{183}{181}=\left(1-\frac{1}{179}\right)+\left(1-\frac{1}{180}\right)+\left(1+\frac{2}{181}\right)\)

\(=3-\left(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}\right)\)

Ta thấy \(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}>0\)suy ra \(3-\left(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}\right)< 3\)

Khi đó \(\frac{178}{179}+\frac{179}{180}+\frac{183}{181}< 3\)

a) A=\(\frac{178}{179}+\frac{179}{180}+\frac{183}{181}\)

ta có :

 \(A=\left(1-\frac{1}{179}\right)+\left(1-\frac{1}{180}\right)+\left(1+\frac{2}{181}\right)\)

 \(\Rightarrow A=\left(1+1+1\right)-\left(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}\right)\)

\(\Rightarrow A=3-\left(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}\right)< 3\)

Vậy \(A< 3\)

a. Ta có :

\(\frac{178}{179}< 1\left(\frac{1}{179}\right)\)

\(\frac{179}{180}< 1\left(\frac{1}{180}\right)\)

\(\frac{183}{181}>1\left(\frac{3}{181}\right)\left(1\right)\)

Mà \(\frac{3}{181}>\frac{1}{179}+\frac{1}{180}\left(=\frac{359}{32220}< \frac{3}{181}\right)\left(2\right)\)

Từ \(\left(1\right)\&\left(2\right)\Rightarrow\frac{178}{179}+\frac{179}{180}+\frac{183}{181}< 1+1+1\)

Vậy \(A< 3\)

b) \(A=\frac{1+5+5^2+5^3+...+5^{10}+5^{11}}{1+5+5^2+5^3+...+5^9+5^{10}}=5^{11}\)

bn rút gọn là dc  

\(B=\frac{1+7+7^2+7^3+...+7^{10}+7^{11}}{1+7+7^2+7^3+...+7^9+7^{10}}=7^{11}\)

\(A=5^{11},B=7^{11}\)

\(\Rightarrow7^{11}>5^{11}\Rightarrow B>A\)

hk tốt #

Lời giải:

$\frac{179}{197}< 1< \frac{971}{917}$

$\frac{183}{184}> 0> \frac{-184}{183}$

1/Vì 179/197<1 ; 971/917>1

=>179/197<971/917

2/Vì 183/184<1 ; 184/183>1

=>183/184<184/183

3/Ta có : -3/31=-3*101/31*101=-303/3131

Vì -303>-789 =>-303/3131>-789/3131 =>-3/31>-789/3131

1/>

2/<

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Duyệt lẹ !Duyệt lẹ !Duyệt lẹ !

\(\dfrac{-178}{179}>-1>\dfrac{-191}{189}\\ \dfrac{127}{129}=1-\dfrac{2}{129};\dfrac{871}{873}=1-\dfrac{2}{873}\\ \dfrac{2}{129}>\dfrac{2}{873}\left(129< 873\right)\Leftrightarrow1-\dfrac{2}{129}< 1-\dfrac{2}{873}\Leftrightarrow\dfrac{127}{129}< \dfrac{871}{873}\)

\(A=\frac{4\cdot0,125\cdot20,2\cdot800\cdot0,25}{1,01\cdot75+0,26\cdot101-1,01}\)   

\(=\frac{4\cdot0,25\cdot0,125\cdot800\cdot20,2}{1,01\cdot75+0,26\cdot100\cdot1,01-1,01}\)   

\(=\frac{1\cdot100\cdot20,2}{1,01\cdot\left(75+26-1\right)}\)   

\(=\frac{100\cdot20,2}{100\cdot1,01}\)   

= 20 

\(B=\left(\frac{178}{179}+\frac{179}{180}+\frac{180}{181}\right)\cdot\left(\frac{80}{56}-\frac{15}{12}:\frac{7}{8}\right)\)   

\(=\left(\frac{178}{179}+\frac{179}{180}+\frac{180}{181}\right)\cdot\left(\frac{10}{7}-\frac{5}{4}\cdot\frac{8}{7}\right)\)   

\(=\left(\frac{178}{179}+\frac{179}{180}+\frac{180}{181}\right)\cdot\left(\frac{10}{7}-\frac{10}{7}\right)\)   

\(=\left(\frac{178}{179}+\frac{179}{180}+\frac{180}{181}\right)\cdot0\)   

= 0 

a) 179/197 là số bé

    971/917 là số lớn

=>179/197<971/917

b)183/184 là số bé

   -184/-183=184/183 là số lớn

=> 183/184<184/183

a) Do 179/197 < 1

971/917 > 1

=> 179/197 < 971/917

b) Do 183/184 < 1

-184/-183 = 184/183 > 1

=> 183/184 < -184/-183

a,Vì

179/197 < 1

971/917 > 1

=>179/197 <1<971/917

=>179/197<971/917

b, Vì

183/184 < 1

-184/-183 = 184/183 > 1

=>183/184 <1<184/183

=>183/184<-184/183

Chúc bạn học giỏi nha!!!

1) Ta có: \(\frac{179}{197}<1;\frac{971}{917}>1\)

=> \(\frac{179}{197}<1<\frac{971}{917}\)

=> \(\frac{179}{197}<\frac{971}{917}\)

2) Ta có: \(\frac{183}{184}<1;\frac{184}{183}>1\)

=> \(\frac{183}{184}<1<\frac{184}{183}\)

=> \(\frac{183}{184}<\frac{184}{183}\)

Câu 1:

1) 179/197 và 971/917

Ta có:

\(1-\frac{179}{197}=\frac{18}{197}\)

\(1-\frac{971}{917}=\frac{-54}{917}\)

Mà \(\frac{-54}{917}<\frac{18}{197}\)

\(\Rightarrow\frac{971}{917}<\frac{179}{197}\)

Câu 2:

Ta có:

\(1-\frac{183}{184}=\frac{1}{184}\)

\(1-\frac{184}{183}=\frac{-1}{183}\)

Mà:\(\frac{-1}{183}<\frac{1}{184}\)

\(\Rightarrow\frac{184}{183}<\frac{183}{184}\)

  a) 4/15 và 7/18

 Quy đồng mẫu số giống nhau (4/15)×6, (7/18)×5

Ta đc

   24/90 < 35/90

4/15    <    7/18 (Tu quy dong roi tinh)

115/116    <      575/574 (Vi 575/574>1 con 115/116<1)

178/179    <        256/257 (Tu quy dong roi tinh )

b ) 115/116 và575/574

115 <116 nên 115/116 < 1

 575>574 NÊN 575/574 >1

 VÂỴ  115/116 < 575/574