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Đặt D=2^2021+2^2020+...+2+1

=>2D=2^2022+2^2021+...+2^2+2

=>D=2^2022-1

=>C=2^2022-2^2022+1=1

3 tháng 5 2023

B = \(\dfrac{1}{2002}\) + \(\dfrac{2}{2021}\) + \(\dfrac{3}{2020}\)+...+ \(\dfrac{2021}{2}\) + \(\dfrac{2022}{1}\)

B = \(\dfrac{1}{2002}\) + \(\dfrac{2}{2021}\) + \(\dfrac{3}{2020}\)+...+ \(\dfrac{2021}{2}\) + 2022

B = 1 + ( 1 + \(\dfrac{1}{2022}\)) + ( 1 + \(\dfrac{2}{2021}\)) + \(\left(1+\dfrac{3}{2020}\right)\)+ ... + \(\left(1+\dfrac{2021}{2}\right)\) 

B = \(\dfrac{2023}{2023}\) + \(\dfrac{2023}{2022}\) + \(\dfrac{2023}{2021}\) + \(\dfrac{2023}{2020}\) + ...+ \(\dfrac{2023}{2}\) 

B = 2023 \(\times\) ( \(\dfrac{1}{2023}\) + \(\dfrac{1}{2022}\) + \(\dfrac{1}{2021}\) + \(\dfrac{1}{2020}\)+ ... + \(\dfrac{1}{2}\))

Vậy B > C 

 

27 tháng 1 2023

A=20222−20212+20202−20192+...+22−1�=20222-20212+20202-20192+...+22-1

=(2022−2021)(2022+2021)+(2020−2019)(2020+2019)+....+(2−1)(2+1)=(2022-2021)(2022+2021)+(2020-2019)(2020+2019)+....+(2-1)(2+1)

=1.4043+1.4039+.....+1.3=1.4043+1.4039+.....+1.3

Vì từ 3→40433→4043 có 10111011 số

⇒A=(4043+3).10112⇒�=(4043+3).10112

=4046.10112=2023.1011=4046.10112=2023.1011

=2045253

\(2A=\dfrac{2^{2021}-1-1}{2^{2021}-1}=1-\dfrac{1}{2^{2021}-1}\)

\(2B=\dfrac{2^{2022}-1-1}{2^{2022}-1}=1-\dfrac{1}{2^{2022}-1}\)

mà \(2^{2021}-1< 2^{2022}-1\)

nên A<B

27 tháng 2 2022

A=22020-122021-1

⇒2A=2.(22020-1)22021-1

⇒2A=22021-222021-1

⇒2A=22021-1-122021-1

⇒2A=1-122021-1

B=22021-122022-1

⇒2B=2.(22021-1)22022-1

4 tháng 3 2022

Đây dang lớp mấy vây

\(2.A=\frac{2^{2021}-2}{2^{2021}-1}=1-\frac{1}{2^{2021}-1}\)

\(2B=\frac{2^{2022}-2}{2^{2022}-1}=1-\frac{1}{2^{2022}-1}\)

dó \(\frac{1}{2^{2022}-1}< \frac{1}{2^{2021}-1}\Rightarrow1-\frac{1}{2^{2022}-1}>1-\frac{1}{2^{2021}-1}\Rightarrow A< B\)

HT

B/A

\(=\dfrac{1+\dfrac{2020}{2}+1+\dfrac{2019}{3}+...+1+\dfrac{1}{2021}+1}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}+\dfrac{1}{2022}}\)

\(=\dfrac{2022\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}+\dfrac{1}{2022}\right)}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2021}+\dfrac{1}{2022}}=2022\)

24 tháng 7 2021

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