15199 =  15199

15150 = 2.3.5².101

ƯCLN(15199; 15150) = 1

A = \(\dfrac{1}{2^2}\) + \(\dfrac{1}{3^2}\) + ... + \(\dfrac{1}{10^2}\) < 1

\(\dfrac{1}{2^2}\)  \(< \dfrac{1}{1.2}\) = \(\dfrac{1}{1}-\dfrac{1}{2}\)

\(\dfrac{1}{3^2}\) < \(\dfrac{1}{2.3}=\dfrac{1}{2}-\dfrac{1}{3}\)

\(\dfrac{1}{4^2}\)  < \(\dfrac{1}{3.4}\) =  \(\dfrac{1}{3}-\dfrac{1}{4}\)

......< .......................

\(\dfrac{1}{9^2}\) < \(\dfrac{1}{8.9}\) = \(\dfrac{1}{8}\) - \(\dfrac{1}{9}\)

\(\dfrac{1}{10^2}\) < \(\dfrac{1}{9.10}\) = \(\dfrac{1}{9}-\dfrac{1}{10}\)

Cộng vế với vế ta có:

\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{10^2}\) < \(1-\dfrac{1}{10}\) < 1 (đpcm)

Đặt vế trái bằng A

Ta có\(\dfrac{1}{2^2}\)=\(\dfrac{1}{4}\)

\(\dfrac{1}{3^2}\)<\(\dfrac{1}{2.3}\)

\(\dfrac{1}{4^2}\)<\(\dfrac{1}{3.4}\)

........

\(\dfrac{1}{10^2}\)<\(\dfrac{1}{9.10}\)

vậy A< \(\dfrac{1}{4}\)+\(\dfrac{1}{2}\)-\(\dfrac{1}{10}\)=\(\dfrac{13}{20}\)<1

a; \(\dfrac{64}{85}\) < \(\dfrac{73}{85}\) < \(\dfrac{73}{81}\) 

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

A = \(\dfrac{-8}{n-7}\) 

Để A là phân số thì n \(\in\) Z; n ≠ 7

a) [(-18) + (-17)] : 5

= -35 : 5

= -7

b) 666 - (-422) - 100 - 88

= 666 + 422 - 188

= 1088 - 188

= 900

c) (30 - 20).(-2).2 - 6.(-7 - 3)

= 10.(-4) - 6.(-10)

= 10.(-4 + 6)

= 10.2

= 20

d) 105 - 301 + (-129) - (-255)

= (105 + 255) - (301 + 129)

= 360 - 430

= -70

Bài 10:

a; 152 + (-73) - (-18) - 127

=  152 - 73 + 18 - 127

= (152 + 18) - (73 + 127)

= 170 - 200

= -30

b; 7 + 8 + (- 9) + (-10)

  = 15 - 9 - 10

= 6 - 10

= - 4

Bài 11: -156 - \(x\)

a; Nếu \(x\) = - 26 thì - 156 - \(x\) = -156 - (-26) =  - 156 + 26 = - 130

b; Nếu \(x\) = 76 thì - 156 - \(x\) = -156 - 76 = - 232

c; Nếu \(x\) = - 28 - (-143) = -28 + 143  = 115

Thì - 156 - \(x\) = - 156 - 115 = - 271

Bài 5: 

a. 125 - 5(4 + x) = 15

5(4 + x) = 125 - 15

5(4 + x) = 110

4 + x = 110 : 5

4 + x = 22

x = 22 - 4

x = 18

b. 2³ + (x - 3²) = 5³ - 4³

8 + (x - 9) = 125 - 64

8 + (x - 9) = 61

x - 9 = 61 - 8 

x - 9 = 53

x = 53 + 9

x = 62.

c. 4(x - 5) - 2³ = 2⁴.3

4(x - 5) - 8 = 16.3

4(x - 5) - 8 = 48

4(x - 5) = 48 + 8

4(x - 5) = 56

x - 5 = 56 : 4

x - 5 = 14

x = 14 + 5

x = 19

d. 5(x + 7) - 10 = 2³.5

5(x + 7) - 10 = 8.5

5(x + 7) - 10 = 40

5(x + 7) = 40 + 10

5(x + 7) = 50

x + 7 = 50 : 5

x + 7 = 10

x = 10 - 7

x = 3.

e. 7² - 7(13 - x) = 14

7(13 - x) = 7² - 14

7(13 - x) = 49 - 14

7(13 - x) = 35

13 - x = 35 : 7

13 - x = 5

x = 13 - 5

x = 8

f. 5x - 5² = 10

5x - 25 = 10

5x = 10 + 25

5x = 35

x = 35 : 5

x = 7

Bài 6:

a. 15 : (x + 2) = 3

x + 2 = 15 : 3

x + 2 = 5

x = 5 - 2

x = 3

b. 20 : (1 + x) = 2

1 + x = 20 : 2

1 + x = 10

x = 10 - 1

x = 9

 c. 240 : (x - 5) = 2².5² - 20

240 : (x - 5) = 4.25 - 20

240 : (x - 5) = 100 - 20

240 : (x - 5) = 80

x - 5 = 240 : 80

x - 5 = 3

x = 3 + 5

x = 8

d. 96 - 3(x + 1) = 42

3(x + 1) = 96 - 42

3(x + 1) = 54

x + 1 = 54 : 3

x + 1 = 18

x = 18 - 1

x = 17

e. 5(x + 35) = 515

x + 35 = 515 : 5

x + 35 = 103

x = 103 - 35

x = 68

f. 12x - 33 = 3².3³

12x - 33 = 9.27

12x - 33 = 243

12x = 243 + 33

12x = 276

x = 276 : 12

x = 23

a) 70 - 5.( x - 3 ) = 45

5. ( x - 3 ) = 70 - 45

5. ( x - 3 ) = 25

x - 3 = 25 : 5

x - 3 = 5

x = 5 + 3

x = 8

_________

b) 12 + ( 5  + x ) = 20

5 + x = 20 - 12

5 + x = 8

x = 8 - 5

x = 3

_________

c) 130 - ( 100 + x ) =25

100 + x = 130 - 25

100 + x = 105

x = 105 - 100

x = 5

_________

d) 175 + ( 30 - x ) = 200

30 - x = 200 - 175

30 - x =  25

x = 30 - 25

x = 5

_________

e) 5 ( x + 12 ) + 22 = 92

5 ( x + 12 ) = 92 - 22

5 ( x + 12 ) = 80

x + 12 = 80 : 5

x + 12 = 16

x = 16 - 12

x = 4

___________

f) 95 - 5 ( x + 2 ) = 45

5 ( x + 2 ) = 95 - 45

5 ( x + 2 ) = 50

x + 2 = 50 : 5

x + 2 = 10

x = 10 - 2

x = 8

Sửa câu e):

5 ( x + 12 ) + 22 = 92

5 ( x + 12 ) = 92 - 22

5 ( x + 12 ) = 70

x + 12 = 70 : 5

x + 12 = 14

x = 14 - 12

x = 2

Trên tia gì hả bạn?