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 \(S\)\(>\frac{2019}{2010}\)

Đặt A = 1.2 + 2.3 + 3.4 + ... + 2019.2020 + 2020.2021

=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 2019.2020.3 + 2020.2021.3

=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 2019.2020.(2021 - 2018) + 2020.2021.(2022 - 2019)

=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 2019.2020.2021 - 2018.2019.2020 + 2020.2021.2022 - 2019.2020.2021

=> 3A = 2020.2021.2022

=> A = 2 751 551 080

Đặt \(A=1.2+2.3+3.4+.........+2019.2020+2020.2021\)

\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+.....+2019.2020.3+2020.2021.3\)

\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+.....+2020.2021.\left(2022-2019\right)\)

\(=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2020.2021.2022-2019.2020.2021\)

\(=2020.2021.2022\)

\(\Rightarrow A=\frac{2020.2021.2022}{3}\)

Bạn tham khảo bài giải dưới nhé

Cre: Olm

Hc tốt:)

2+6+12+20+30= 70

Gọi biểu thức trên là A, ta có :

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

Gọi biểu thức trên là A, ta có :

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

đưa ra dạng tổng quát giúp mk nhé thank you

Đặt A=1.2+2.3+3.4+...+99.100
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
3A=99.100.101
A=333300

S = 1.2 + 2.3 + 3.4+.....+99.100

3S=1.2.3+2.3.(4-1) + ..... + 99.100.(101-98)

3S = 1.2.3 + 2.3.4 - 1.2.3 + 99.100.101-98.99.100

3S = 99.100.101 = 999900

S = 999900 : 3  = 333300

333300 

tích nha

Gọi biểu thức trên là A, ta có :

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

sai thì thui nhá,mk hok ngu lắm

ahihi