A=1+2¹+2² +...+2²⁰²¹

2A = 2( 1+2¹+2² +...+2²⁰²¹ )

2A = 2 + 2² + 2³ + ... + 2²⁰²²

2A - A = ( 2 + 2² + 2³ + ... + 2²⁰²² ) - ( 1+2¹+2² +...+2²⁰²¹ )

A = 2²⁰²² - 1

2^x = A + 1 

=> 2^x = 2²⁰²² - 1 + 1 

=> 2^x = 2²⁰²² 

=> x = 2022

Vậy x = 2022

2A=2+2^2+...+2^2022

=>A=2^2022-1

2^x=A+1

=>2^x=2^2022

=>x=2022

có 2 cái 2^1 kìa sửa lai đi

a: \(A=\left(\dfrac{1}{99}+1\right)+\left(\dfrac{2}{98}+1\right)+...+\left(\dfrac{98}{2}+1\right)+1\)

\(=\dfrac{100}{99}+\dfrac{100}{98}+...+\dfrac{100}{2}+\dfrac{100}{100}\)

\(=100\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{100}\right)\)=100B

=>B/A=1/100

b: \(A=\left(\dfrac{1}{49}+1\right)+\left(\dfrac{2}{48}+1\right)+\left(\dfrac{3}{47}+1\right)+...+\left(\dfrac{48}{2}+1\right)+\left(1\right)\)

\(=\dfrac{50}{49}+\dfrac{50}{48}+....+\dfrac{50}{2}+\dfrac{50}{50}\)

\(=50\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{50}\right)\)

\(B=\dfrac{2}{2}+\dfrac{2}{3}+\dfrac{2}{4}+...+\dfrac{2}{49}+\dfrac{2}{50}\)

\(=2\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{49}+\dfrac{1}{50}\right)\)

=>A/B=25

GIÚP MÌNH VỚI ,MÌNH CẦN GẤP!!!

\(1,\text{Áp dụng Mincopxki: }\\ Q\ge\sqrt{\left(a+\dfrac{1}{a}\right)^2+\left(b+\dfrac{1}{b}\right)^2}\ge\sqrt{2^2+2^2}=\sqrt{8}=2\sqrt{2}\\ \text{Dấu }"="\Leftrightarrow a=b\)

\(2,\text{Áp dụng BĐT Cauchy-Schwarz: }\\ P\ge\dfrac{9}{a^2+b^2+c^2+2ab+2bc+2ca}=\dfrac{9}{\left(a+b+c\right)^2}\ge\dfrac{9}{1}=9\\ \text{Dấu }"="\Leftrightarrow a=b=c=\dfrac{1}{3}\)

b) A  = 2⁰ +2¹ +2²+...+2³⁰

=> 2A = 2¹ +2²+2³+...+2³¹

=> 2A-A = 2³¹-2⁰

=> A = 2³¹ - 1 = B

c) A = 2⁰ +2¹+2²+...+2¹⁰⁰

=>2A = 2¹+2²+2³+...+2¹⁰¹

=> 2A-A = 2¹⁰¹-2⁰

A = 2¹⁰¹ - 1

=> A + 1 = 2¹⁰¹

mà A+ 1 = 2^x

=> x = 101