-11/15>-1

-19/7<-1

-23/-27>-1

-2012/1994<-1

a, Ta có: \(\frac{23}{27}>\frac{23}{29}>\frac{22}{29}\)

\(\Rightarrow\frac{23}{27}>\frac{22}{29}\)

b, Ta có:

\(\frac{12}{25}< \frac{1}{2}\)

\(\frac{25}{49}>\frac{1}{2}\)

\(\Rightarrow\frac{12}{25}< \frac{25}{49}\)

B1:

a,<    b,<

c,<    d,>

e,>    g,>

B2:

a,<    b,<

c,<

b1

a, <

b, <

c, <

d,>

e,>

g, >

a, <

b, <

c,<

a: (-21)*(-5)=105

(-34)*(-3)=102

=>(-21)*(-5)>(-34)*(-3)

b: -47*12=-564

27*(-22)=-594

=>-47*12>-27*22

c: (-4)*(-19)=76

15*8=120

=>(-4)*(-19)<15*8

d: -(17*3)=-51<-46=-23*2

a)(-21).(-5) > (-34).(-3)                        c)(-4).(-19) < 15.8

b)(-47).12 > 27.(-22)                          d)-(17.3) < -23.2

Số số hạng của tổng A là : \(\dfrac{30-21}{1}+1=10\left(sh\right)\)

`=>A=\underbrace{1/21+1/22+...+1/30}_{10sh}>\underbrace{1/30+1/30+1/30+...+1/30}_{10sh}`

`=>A>(1)/(30).10`

`=>A>10/30`

`=>A>1/3`

`=>đpcm`

a, Ta có: \(\frac{29}{60}< \frac{30}{60}=\frac{1}{2}=\frac{14}{28}< \frac{15}{28}\) . Vậy \(\frac{29}{60}< \frac{15}{28}\)

b, \(\frac{13}{30}< \frac{15}{30}=\frac{1}{2}=\frac{21}{42}< \frac{23}{42}\).Vậy \(\frac{13}{30}< \frac{23}{42}\)

c, \(\frac{13}{36}>\frac{12}{36}=\frac{1}{3}=\frac{15}{45}>\frac{14}{45}\).Vậy \(\frac{13}{36}>\frac{14}{45}\)

d, \(\frac{1919}{9595}=\frac{1}{5}=\frac{1010}{5050}< \frac{1111}{5050}.\)Vậy \(\frac{1919}{9595}< \frac{1111}{5050}\)

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

never gonna give you up

never gonna let you down

never gonna run around

desert you

never gonna make you cry

never gonna say goodbye

never gonna tell a lie 

and hurt you :)

SOS

$S=1+2+2^2+...+2^9$

$2S=2\left(1+2+2^2+...+2^{10}\right)$

$2S=2+2^2+2^3+...+2^9$

$2S-S=\left(2+2^2+2^3+...+2^{10}\right)-\left(1+2+2^2+...+2^9\right)$

\(S=2^{10}-1=2^2.2^8-1=4.2^8-1

HT

$S=1+2+2^2+...+2^9$

$2S=2\left(1+2+2^2+...+2^{10}\right)$

$2S=2+2^2+2^3+...+2^9$

$2S-S=\left(2+2^2+2^3+...+2^{10}\right)-\left(1+2+2^2+...+2^9\right)$

\(S=2^{10}-1=2^2.2^8-1=4.2^8-1