AI NHANH MÌNH K , ĐANG CẦN GẤP

a)xét 2A =2+2^2+2^3+.....+2^2019

-A=1+2+2^2+...+2^2018

A=(2^2019)-1 <2^2019

b)theo câu a ta có A+1=2^2019-1+1=2^2019=2^(x+1)

2019=x+1 =>x=2018

c)theo câu b ta có A+1=2^2019=2.4^x=2^(1+2x)

=>2019=1+2x

tự làm nốt

\(A=\frac{1}{2^2}+\frac{1}{3^2}+.....+\frac{1}{2018^2}\)

\(< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{2017\cdot2018}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2017}-\frac{1}{2018}\)

\(=1-\frac{1}{2018}\)

\(=\frac{2017}{2018}< \frac{3}{4}\)

Ta có :

\(2A=2+2^2+2^3+...+2^{2018}\)

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

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

Vậy A<B

Ko ghi đề

\(2A=2+2^2+...+2^{101}\\ 2A-A=2^{101}-1\\ =>A=2^{101}-1\)

Mấy cái khác cg lm như v (b thì 3b)

Nhớ đúng mk nhá

Bài 1: 

a) 0²⁰⁰² < 0²⁰²³

b) 2022⁰ = 2023⁰

c) 54⁹ < 55¹⁰

d) ( 4 + 5 )³ > 4² + 5²

đ) 9² - 3² > ( 9 - 3 )²

Bài 2:

a) 3² x 4³ - 3² + 333

= 9 x 64 - 9 + 333

= 576 - 9 + 333

= 567 + 333

= 900

b) 5 x 4³ + 24 x 5 + 41⁰

= 5 x 64 + 24 x 5 + 1

= 5 x ( 64 + 24 ) + 1

= 5 x 88 + 1

= 440 + 1

= 441

c) 2³ x 4² + 3² x 5 - 40 x 1²⁰²³

= 8 x 16 + 9 x 5 - 40 x 1

= 128 + 45 - 40

= 133

Bài 1 :

a) \(0^{2002}=0;0^{2023}=0\Rightarrow0^{2002}=0^{2023}\)

b) \(2022^0=1;2023^0=1\Rightarrow2022^0=2023^0\)

c) \(54^9< 55^9;55^9< 55^{10}\Rightarrow54^9< 55^{10}\)

d) \(\left(4+5\right)^3>\left(4+5\right)^2;\left(4+5\right)^2>4^2+5^2\Rightarrow\left(4+5\right)^3>4^2+5^2\)

đ) \(9^2-3^2=81-9=82;\left(9-3\right)^2=6^2=36\Rightarrow9^2-3^2>\left(9-3\right)^2\)

Bài 2 :

a) \(3^2.4^3-3^2+333=3^2\left(4^3-1\right)+9.37=9.63+9.37=9\left(63+37\right)=9.100=900\)

b) \(5.4^3+24.5+41^0=20.4^2+20.6+1=20\left(16+6\right)+1=20.22+1=441\)

c) \(2^3.4^2+3^2.5-40.1^{2023}=8.16+9.5-40.1=128+45-40=128+5=133\)

\(A=2^0+2^1+2^2+2^3+...+2^{2010}\)

\(A=1+2+2^2+2^3+...+2^{2010}\)

\(2A=2+2^2+2^3+...+2^{2011}\)

\(2A-A=\left[2+2^2+2^3+...+2^{2011}\right]-\left[1+2+2^2+2^3+...+2^{2010}\right]\)

\(A=2^{2011}-1\)

Mà \(B=2^{2011}-1\)

=> A = B

Ta có: A=\(2^0+2^1+2^2+2^3+...+2^{2010}\)

          2A=\(2^1+2^2+2^3+2^4+...+2^{2011}\)

     2A-A hay A=\(2^{2011}-2^0\)

                       =\(2^{2011}-1\)

Vì \(2^{2011}-1=2^{2011}-1\)

\(\Rightarrow\)A=B

Hok tốt nha!!!

`A``=``2^0``+`2^1``+``2^2``+`2^3``+`...`+``2^(2010)`

`2A=2^1+2^2+2^3+2^4+...+2^(2011)`

`2A-A=(2^1+2^2+2^3+2^4+...+2^(2011))-(2^0+2^1+2^2+2^3+...+2^(2010)`

`A=2^(2011)-1`

`A=B`