Nguồn: Tính tổng: 1x2 + 2x3 + 3x4 +...+ 2019x2020 + 2020x2021 - Hoc24
Đặt $A=1.2+2.3+3.4+.........+2019.2020+2020.2021$

$\Rightarrow 3A=\mathrm{1.2.3}+\mathrm{2.3.3}+\mathrm{3.4.3}+.....+\mathrm{2019.2020.3}+\mathrm{2020.2021.3}$

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

$=\mathrm{1.2.3}+\mathrm{2.3.4}-\mathrm{1.2.3}+\mathrm{3.4.5}-\mathrm{2.3.4}+...+\mathrm{2020.2021.2022}-\mathrm{2019.2020.2021}$

$=\mathrm{2020.2021.2022}$

$\Rightarrow A=\frac{\mathrm{2020.2021.2022}}{3}$

\(C=\dfrac{2}{1\times2}+\dfrac{2}{2\times3}+...+\dfrac{2}{2019\times2020}\)

\(=2\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{2019\times2020}\right)\)

\(=2\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2019}-\dfrac{1}{2020}\right)\)

\(=2\left(1-\dfrac{1}{2020}\right)=2.\dfrac{2019}{2020}=\dfrac{2019}{1010}\)

lớp 5 đây á

no no

đây ko phải lớp 5 mọi người nhỉ ?

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 \(S\)\(>\frac{2019}{2010}\)

Bạn tham khảo bài giải dưới nhé

Cre: Olm

Hc tốt:)

A= 1x2+2x3+3x4+...+98x99 A x 3= 1x2 x (3-0) +2x3x (4-1)+3x4 x (5-2)+...+98x99x (100-97) = 1x2x3+2x3x4+......98x99x100- (1x2x0+ 2x3x1+....+ 98x99x97) = 98x99x100

A= 1x2+2x3+3x4+...+98x99
A x 3= 1x2 x (3-0) +2x3x (4-1)+3x4 x (5-2)+...+98x99x (100-97)
= 1x2x3+2x3x4+......98x99x100- (1x2x0+ 2x3x1+....+ 98x99x97)
= 98x99x100.

Đặt A = 1×2 + 2×3 + 3×4 + ... + 19×20

⇒ 3A = 1×2×3 + 2×3×3 + 3×4×3 + ... + 19×20×3

= 1×2×3 + 2×3×(4 - 1) + 3×4×(5 - 2) + ... + 19×20×(21 - 18)

= 1×2×3 - 1×2×3 + 2×3×4 - 2×3×4 + 3×4×5 - ... - 18×19×20 + 19×20×21

= 19×20×21

= 7980

⇒ A = 7980 : 3 = 2660

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

A = 333 300 nhé bn

333300

**** mik nha bak