\(4^{127}=4\cdot4\cdot4\cdot4\cdot4\cdot...\cdot4\cdot4=2,894802231e\)

\(81^{43}=81\cdot81\cdot81\cdot81\cdot81\cdot...\cdot81\cdot81=1,16106307e\)

\(\Rightarrow4^{127}< 81^{43}\)

Ta có 4¹²⁷=(4³)⁴²*4=64⁴²*4

         81⁴³=81⁴²*81

81⁴²>64⁴²   ;    81>4

\(\Rightarrow81^{42}\cdot81>64^{42}\cdot4\Rightarrow81^{43}>4^{127}\)

4 ¹²⁷< 4¹²⁹=(4³)⁴³=64⁴³

Vi 64⁴³<81⁴³

=.> 4¹²⁷< 81⁴³

Có : 81^43 = (3^4)^43 = 3^172 < 4^2017

=> 81^43 < 4^2017 

Vậy 81^43 < 4^2017

bdhzsmjdsbjksdjbkjks

\(1-\frac{43}{44}\)=\(\frac{1}{44}\)

\(1-\frac{65}{66}=\frac{1}{66}\)

\(\frac{1}{44}>\frac{1}{66}\)

=> \(\frac{43}{44}>\frac{65}{66}\)

a/ \(27^{11}=\left(3^3\right)^{11}=3^{33}\); \(81^8=\left(3^4\right)^8=3^{32}< 3^{33}\Rightarrow81^8< 27^{11}\)

b/ \(3^{2n}=\left(3^2\right)^n=9^n\); \(2^{3n}=\left(2^3\right)^n=8^n< 9^n\Rightarrow2^{3n}< 3^{2n}\)

a. 27¹¹= (3³)¹¹ = 3³³

    81⁸ = (3⁴)⁸ = 3³²

Suy ra 3³³>3³² hay 27¹¹>81⁸

b. 3²ⁿ = (3²)ⁿ = 9ⁿ

     2³ⁿ = (2³)ⁿ = 8ⁿ

Mà 9>8 suy ra 9ⁿ>8ⁿ hay 3²ⁿ>2³ⁿ

c. 5²³ = 5²² . 5

   (6.5)²² = 6²² . 5²²

Vì 6²²>5 suy ra 5²² . 5<6²² . 5²² hay 5²³<(6.5)²²

d. 72⁴⁵-72⁴⁴ = 72⁴⁴(72-1) = 72⁴⁴ . 71

    72⁴⁴-72⁴³ = 72⁴³(72-1) = 72⁴³ . 71

Vì 72⁴⁴>72⁴³ suy ra 72⁴⁴ . 71>72⁴³ . 71 hay 72⁴⁵-72⁴⁴>72⁴⁴-72⁴³

a) Ta có: 27¹¹= (3³)¹¹=3³³

81⁸=(3⁴)⁸=3³²

^{Suy ra:} 27¹¹>81⁸

^{Mình chỉ làm cho bn 1 ví dụ thôi. các bài còn lại bn làm tương tự nhé!}

a) 81⁸= 27²⁴

suy ra 81⁸ > 27¹¹

b) đề sai

c) 5²³= 5. 5²²

mà 6> 5

suy ra 6.5²²> 5²³

d)72⁴⁵ - 72⁴⁴ = 72⁴⁴( 72 -1) = 72⁴⁴. 71

72⁴⁴ - 72⁴³ = 72⁴³(72-1) = 72⁴³ . 71

mà 72^{43 <}72⁴⁴

^{suy ra} 72⁴⁵ - 72⁴⁴ >72⁴⁴ - 72⁴³

câu a bằng 94

câu b (-105)+79<(-12)+(-23)

a) \(4.5^2-81:3^2-\left|-3\right|=4.25-81:9-3\)

                                                 \(=100-9-3\)

                                                \(=88\)

b) Ta có: \(-105+79=-26\)

       \(-12+\left(-23\right)=-35\)

Vì \(-35< -26\)nên \(-105+79>-12+\left(-23\right)\)

_Học tốt nha_

a) \(\dfrac{43}{47}=\dfrac{47-4}{47}=\dfrac{47}{47}-\dfrac{4}{47}=1-\dfrac{4}{47}\)

\(\dfrac{53}{57}=\dfrac{57-4}{57}=\dfrac{57}{57}-\dfrac{4}{57}=1-\dfrac{4}{57}\)

Vì \(\dfrac{4}{47}>\dfrac{4}{57}\)=>\(1-\dfrac{4}{47}< 1-\dfrac{4}{57}\)

=>\(\dfrac{43}{47}< \dfrac{53}{57}\)

b) Ta chọn phân số trung gian là: \(\dfrac{64}{81}\)

Vì \(\dfrac{64}{81}>\dfrac{64}{85}\)

Mà \(\dfrac{64}{81}< \dfrac{73}{81}\)

=> \(\dfrac{64}{85}< \dfrac{64}{81}< \dfrac{73}{81}\)

Vậy \(\dfrac{64}{85}< \dfrac{73}{81}\)

c) Ta chọn phân số trung gian là: \(\dfrac{18}{37}\)

Vì \(\dfrac{18}{37}>\dfrac{15}{37}\)

Mà \(\dfrac{18}{37}< \dfrac{18}{31}\)

=> \(\dfrac{15}{37}< \dfrac{18}{37}< \dfrac{18}{31}\)

Vậy \(\dfrac{18}{31}>\dfrac{15}{37}\)

Phần d) mình không biết lời giải

Bài 1b:

\(\frac31\) + \(\frac33\) + \(\frac36\) + \(\frac{3}{10}\) + ...+\(\frac{3}{x\left(x+1\right):2}\) = \(\frac{2015}{336}\)

3.(\(\frac11+\frac13+\frac16+\frac{1}{10}+\cdots+\frac{1}{x\left(x+1):2\right.})\) = \(\frac{2015}{336}\)

3.2(\(\frac12+\frac16+\frac{1}{12}+\frac{1}{20}+\cdots+\frac{1}{x\left(x+1\right)})=\) \(\frac{2015}{336}\)

6.(\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\cdots+\frac{1}{x.\left(x+1\right)})\) = \(\frac{2015}{336}\)

6.(\(\frac11-\frac12\) + \(\frac12\)-\(\frac14\) +...+ \(\frac{1}{x}\) - \(\frac{1}{x+1}\)) = \(\frac{2015}{336}\)

6.(\(\frac11\) - \(\frac{1}{x+1}\)) = \(\frac{2015}{336}\)

1 - \(\frac{1}{x+1}\) = \(\frac{2015}{336}\) : 6

1 - \(\frac{1}{x+1}\) = \(\frac{2015}{2016}\)

\(\frac{1}{x+1}\) = 1 - \(\frac{2015}{2016}\)

\(\frac{1}{x+1}\) = \(\frac{1}{2016}\)

\(x+1\) = 2016

\(x\) = 2016 - 1

\(x\) = 2015

Bài 2:

A = \(\frac{6n+1}{4n+3}\) (n ∈ Z\(^{-}\))

A ∈ Z khi và chỉ khi:

(6n + 1) ⋮ (4n + 3)

(12n + 2) ⋮ (4n + 3)

[3(4n + 3) - 7] ⋮ (4n + 3)

7 ⋮ (4n + 3)

(4n + 3) ∈ Ư(7) = {-7; -1; 1; 7}

n ∈ {- 5/2; -1; - 1/2; 1}

Nếu n = - 1 thì A = (-6 + 1)/(-4 + 3) = 5 (loại)

Nếu n = 1 thì: A = (6 + 1).(4+3) = 1 (loại)

Không có giá trị nào thỏa mãn đề bài hay n ∈ ∅