B = A 

mình nghĩ thế

bài này ai giải ra đc ko?

thank you very much ! ^^

S= 2x(1/1x2+1/2x3+1/3x4+...........+1/2020x2021)

S=2x(1-1/2+1/2-1/3+1/3-...+1/2020-1/2021)

S=2x(1-1/2021)

S=2x2020/2021

S=4040/2021

2019/2010<3/2<4040/2021

=>2019/2010<S

S = 2 x (\(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+...+\)\(\frac{2}{2020\times2021}\))

= 2 x (\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\)\(\frac{1}{2020\times2021}\)) 

= 2 x ( \(1-\frac{1}{2021}\))

= \(2\times\frac{2020}{2021}\)

= \(\frac{4040}{2021}\)

= \(\frac{4042-2}{2021}\)

\(=2-\frac{2}{2021}\)

Ta có :

\(\frac{2019}{2010}=\frac{2020-1}{2010}=2-\frac{1}{2010}=2-\frac{2}{2020}\)

Ta thấy \(\frac{2}{2021}< \frac{2}{2020}\)

nên \(2-\frac{2}{2021}>2-\frac{2}{2020}\)

Vậy \(S\)\(>\frac{2019}{2010}\)

Lời giải:
$10A=\frac{10^{2021}-10}{10^{2021}-1}=\frac{10^{2021}-1-9}{10^{2021}-1}$

$=1-\frac{9}{10^{2021}-1}>1$

$10B=\frac{10^{2022}+10}{10^{2022}+1}=\frac{10^{2022}+1+9}{10^{2022}+1}$

$=1+\frac{9}{10^{2022}+1}<1$

$\Rightarrow 10A> 1> 10B$

Suy ra $A> B$

Ta có: \(2y+\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{2020\cdot2021}\right)=\dfrac{4041}{2021}\)

\(\Leftrightarrow2y+\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2020}-\dfrac{1}{2021}\right)=\dfrac{4041}{2021}\)

\(\Leftrightarrow2y+1-\dfrac{1}{2021}=\dfrac{4041}{2021}\)

\(\Leftrightarrow2y=\dfrac{4041}{2021}+\dfrac{1}{2021}-1\)

\(\Leftrightarrow2y=2-1=1\)

hay \(y=\dfrac{1}{2}\)

nhanh nha các bạn

`# \text {DNamNgV}`

\(A=1+2+2^2+...+2^{2021}\text{ và }B=2^{2022}\)

Ta có:

\(A=1+2+2^2+...+2^{2021}\\ \Rightarrow2A=2+2^2+2^3+...+2^{2022}\\\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2022}\right)-\left(1+2+2^2+...+2^{2021}\right)\\ \Rightarrow A=2+2^2+2^3+...+2^{2022}-1-2-2^2-...-2^{2021}\\ \Rightarrow A=2^{2022}-1\)

Vì \(2^{2022}-1< 2^{2022}\)

\(\Rightarrow A< B.\)

A=B

A=1+3+3²+3³+.....+3²⁰²¹
-->3A=3(1+3+3²+3³+.....+3²⁰²¹)
-->3A=3+3²+3³+...+3²⁰²²
-->3A-A=(3+3²+3³+....3²⁰²²)-(1+3+3²+3³+.....+3²⁰²¹)
-->2A=3²⁰²²-1
-->A=(3²⁰²²-1):2
Vì (3²⁰²²-1):2>(3²⁰²²-1):2
-->A=B
 

a) < b) <

a2021/2022<22/21

b.a/b>a/b+1

A. 2021/2022 <1               22/21 > 1

Suy ra 2021/2022 < 22/21

B. a/b và a/b+1 cùng có chung tử số là a. Hai PS có chung tử số, mẫu số càng lớn thì PS càng bé, mẫu số càng bé thì PS càng lớn. b<b+1

nên suy ra a/b > a/b + 1