a) 2,191 > 2,19

b) 5,121 < 5,(12)

c) -4,634 > - 4,6(34)

d) 0,0101 < 0,(01)

a. 2,191 > 2,19 

b. 5,121 < 5, (12)

c) -4,634 > -4,6(34)

d) 0,0101 = 0,(01)

Mình ko chắc đúng

ngu thi dung hoi

 ta có :

\(25^{1008}=\left(5^2\right)^{1008}=5^{2.1008}=5^{2016}\)

mà \(5^{2017}>5^{2016}\)

\(\Rightarrow\)\(5^{2017}>\left(5^2\right)^{1008}\)

\(\Rightarrow\)\(5^{2017}>25^{1008}\)

có \(5^{2017}=\left(5^2\right)^{1008}\times5\)\(=25^{1008}\times5\)

mà \(=25^{1008}\times5\)> \(25^{1008}\)

nên \(5^{2017}>25^{1008}\)

Ta có:

\(5^{2017}>5^{2016}=\text{[}5^2\text{]}^{1008}=25^{1008}\)

Suy ra: 5²⁰¹⁷ > 25¹⁰⁰⁸

Ta có:

\(1-A=1-\frac{10^{101}-1}{10^{102}-1}=\frac{10^{102}-1-\text{[}10^{101}-1\text{]}}{10^{102}-1}=\frac{10^{102}-1-10^{101}+1}{10^{102}-1}\)\(=\frac{10^{102}-10^{101}}{10^{102}-1}=\frac{10^{101}\left[10-1\right]}{10^{101}\text{[}10-\frac{1}{10^{101}}\text{]}}=\frac{10-1}{10-\frac{1}{10^{101}}}=\frac{9}{10-\frac{1}{10^{101}}}\)

\(1-B=1-\frac{10^{100}+1}{10^{101}+1}=\frac{10^{101}+1-\left[10^{100}+1\right]}{10^{101}+1}=\frac{10^{101}+1-10^{100}-1}{10^{100}+1}\)

\(=\frac{10^{101}-10^{100}}{10^{101}+1}=\frac{10^{100}\left[10-1\right]}{10^{100}\text{[}10+\frac{1}{10^{100}}\text{]}}=\frac{10-1}{10+\frac{1}{10^{100}}}=\frac{9}{10+\frac{1}{10^{100}}}\)

Vì \(\frac{9}{10-\frac{1}{10^{101}}}>\frac{9}{10+\frac{1}{10^{100}}}\Rightarrow A< B\)

\(\frac{29}{60}< \frac{4}{9}\)

\(\frac{6}{28}< \frac{101}{400}\)

\(\frac{131313}{393939}=\frac{1}{3}\)

a) ta có: \(\frac{29}{60}=0,483;\frac{4}{9}=0,44\)

\(\Rightarrow0,483>0,44\Rightarrow\frac{29}{60}>\frac{4}{9}\)

b) ta có: \(\frac{6}{28}=\frac{3}{14}=0,21;\frac{101}{400}=0,25\)

\(\Rightarrow0,21< 0,25\Rightarrow\frac{6}{28}< \frac{101}{400}\)

c) ta có: \(\frac{131313}{393939}=\frac{13x10101}{39x10101}=\frac{13}{39}=\frac{1}{3}\)

\(\Rightarrow\frac{131313}{393939}=\frac{1}{3}\)

SO SÁNH

a) 4/9 = 28/63

Tìm phân số trung gian 

Ta có: 29/60 > 29/63 > 28/63

Vậy 29/60 > 28/63 hay 29/60 > 4/9

b) 6/28 = 96/448

Tìm phân số trung gian 

Ta có: 101/400 > 96/400 > 96/448

Vậy 101/400 > 96/448 hay 101/400 > 6/28

c) 131313/393939 = 1/3

Vậy 131313/393939 = 1/3

\(a,2n-3⋮n+1\)

\(\Rightarrow2n+2-5⋮n+1\)

\(\Rightarrow2\left(n+1\right)-5⋮n+1\)

      \(2\left(n+1\right)⋮n+1\)

\(\Rightarrow5⋮n+1\)

\(\Rightarrow n+1\inƯ\left(5\right)=\left\{-1;1;-5;5\right\}\)

\(\Rightarrow n\in\left\{-2;0;-6;4\right\}\)

vậy_

\(b,A=2^0+2^1+2^2+...+2^{100}\)

\(\Rightarrow2A=2^1+2^2+2^3+...+2^{101}\)

\(\Rightarrow2A-A=2^{101}-1\text{ hay }A=2^{101}-1\)

\(2^{101}-1< 2^{101}\)

\(\Rightarrow A< 2^{101}\)

vậy_

2n - 3 chia hết cho n+ 1 

=> 2n + 2 - 5  chia hết cho n + 1 

=> 2(n+1 ) - 5 chia hết cho n + 1 

Mà 2(n+1 ) chia hết cho n + 1  

=>  5 chia hết cho n + 1 

=> n + 1 thuộc Ư(5)= {1; -1 ; 5 ; -5 }

TH1 : n + 1 = 1 => n = 0 

TH2 : n + 1 = -1  => n = -2 

th3 : n + 1 = 5 => n = 4 

TH4 : n + 1 = -5 => n = -6 

=> n thuộc {0;-2;4;6 }

a, 101/102 = 1-1/102 ; 91/92 = 1-1/92 .Ta thấy phần bù của 101/102 bé hơn nên 101/102 lớn hơn .

b, 7/15 = 1-8/15; 8/17 = 1-9/17.Ta thấy phần bù của 8/17 bé hơn nên 8/17 lớn hơn.

b, 91/89 = 1+2/89; 83/81 = 1+2/81.Ta thấy phần hơn của 91/89 bé hơn nên 83/81 lớn hơn.