\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{1000}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{999}}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{999}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{1000}}\right)\)

\(A=1-\frac{1}{2^{1000}}< 1=B\)

`Answer:`

Đặt \(C=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}\)

Ta thấy:

\(\frac{1}{1.2}>\frac{1}{2^2}\)

\(\frac{1}{2.3}>\frac{1}{2^3}\)

\(\frac{1}{3.4}>\frac{1}{2^4}\)

...

\(\frac{1}{999.1000}>\frac{1}{2^{1000}}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{1000}}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}\)

\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-\frac{1}{5}+...+\frac{1}{999}-\frac{1}{1000}\)

\(\Rightarrow A< 1-\frac{1}{1000}\)

Mà \(\frac{1}{1000}>0\)

\(\Rightarrow1-\frac{1}{1000}< 1\)

\(\Rightarrow C< B\)

\(\Rightarrow A< C< B\)

\(\Rightarrow A< B\)

a, \(9^{20}=\left(3^2\right)^{20}=3^{40}\)

\(27^{13}=\left(3^3\right)^{13}=3^{39}\)

mà \(3^{40}>3^{39}\Leftrightarrow9^{20}=27^{13}\)

vậy \(9^{20}=27^{13}\)

9²⁰ = 3⁴⁰ ; 27¹³ = 3³⁹

Vì 40 > 39 nên 3⁴⁰ > 3³⁹ và 9²⁰ > 27¹³

b ) 3¹⁰⁰⁰ = 30¹⁰⁰

     2¹⁵⁰⁰ = 30¹⁰⁰

Vì 100 =100 nên .....

Ta có:\(A=1+2+2^2+2^3+....+2^{2017}.\)

\(\Rightarrow2A=2^1+2^2+2^3+2^4+....+2^{2018}\)

\(\Rightarrow2A-A=\left(2^1+2^2+2^3+2^4+...+2^{2018}\right)-\left(1+2^1+2^2+2^3+...+2^{2017}\right)\)

\(\Rightarrow A=2^{2018}-1\)

\(\Rightarrow A=B\)

a] 2^10 < 8^4

cầm máy tính mà bấm

mk nha,nếu mk có thiếu thì bn cũng cho sai phải ko nhưng bn chỉ bảo là ai nhanh thôi chứ bn có bảo ai đúng đâu,nên mk nha

A=4.8.12+8.12.16+12.16.20+16.20.24

   =4(1.2.3+2.3.4+3.4.5+4.5.6)

   =4B

=> A=4B

Tk cho mk với@@@@@@@@@@

a) -23/-17 = 23/17

-13/-17 = 13/17

Vì 23>13 => 23/17>13/17

Vậy -23/-17>-13/-17

b) -57/53 = -5301/4929

-97/93 = -5141/4929

Vì -5301<-5141 => -5141/4929< -5301/4929

Vậy -97/93<-57/53

c) 81/-89 = -81/89

-21/29 = -1869/2581

-81/89 = -2349/2581

Vì -1869>-2349 => -2349/2581>-1869/2581

Vậy 81/-89>-21/29