1x3 + 2x3 + 3x3 + 4x3 + ....+ 50x3

=(1+2+3+4+...+50)x3

=1275x3

=3825

đúng nha

bạn nhanh thật                                                    

   2023 x 3 + 2023 + 2023 x 6

= 2023 x 3 + 2023 x 1 + 2023 x 6

= 2023 x ( 3 + 1 + 6)

= 2023 x 10

 = 20230 

20230

2023*3+2023+2023*6

= 2023*3+2023*1+2023*6

=2023*[3+1+6]

=2023*10

=20230

$x^4+2023x^2+2022x+2023$

$=x^4-x+2023x^2+2023x+2023$

$=(x^4-x)+(2023x^2+2023x+2023)$

$=x(x^3-1)+2023(x^2+x+1)$

$=x(x-1)(x^2+x+1)+2023(x^2+x+1)$

$=(x^2+x+1)[x(x-1)+2023]$

$=(x^2+x+1)(x^2-x+2023)$

...

\(A=\dfrac{2023^{2022+2}}{2023^{2022-1}}=2023^{2024-2021}=2023^3\\ B=\dfrac{2023^{2022}}{2023^{2022-3}}=2023^3\\ \Rightarrow A=B\left(=2023^3\right)\)

A=1x2+2x3+3x4+...+49x50

3A= 3(1.2+2.3+3.4+...+49.50)

3A= 1.2.3+2.3.3+3.4.3+...+49.50.3

3A= 1.2.(3-0)+2.3(4-1)+3.4(5-2)+...+49.50.(51-48)

3A= 0.1.2-1.2.3+1.2.3-2.3.4+2.3.4-3.4.5+...+48.49.50-49.50.51

3A= 49.50.51

A= 49.50.51/3=41650

B=1x3+3x5+5x7+...+99x101

B=1/1.3 +1/3.5 +...+1/99.101

2B=2/1.3 + 2/3.5 +...+2/99.101

2B=1-1/3+1/3-1/5+...+1/99-1/101

2B=1-1/101

2B=100/101

B=100/101:2=100/202

C=1x2x3+2x3x4+3x4x5+...+50x51x52
Nhân C với 4 ta được:
C x 4 = 1x2x3x4 + 2x3x4x 4 + 3x4x5x4 +…+50x51x52x4
C x 4 = 1x2x3x4 + 2x3x4x(5-1) + 3x4x5x(6-2) + ... + 50x51x52x(53-49)
C x 4 = 1x2x3x4 + 2x3x4x5 - 1x2x3x4 + 3x4x5x6 - 2x3x4x5 + ... +49x 50x51x52 - 50x51x52x53
Sau khi cộng - trừ giản ước ta có : C x 4 = 50x51x52x53
C = 50x51x52x53 : 4 = 1756950

\(3B=1.3^2+2.3^3+3.3^4+...+2022.3^{2023}+2023.3^{2024}\)

\(2B=3B-B=-3-3^2-3^3-...-3^{2023}+2023.3^{2024}\)

\(2B=2023.3^{2024}-\left(3+3^2+3^3+...+3^{2023}\right)\)

Đặt 

\(C=3+3^2+3^3+...+3^{2023}\)

\(3C=3^2+3^3+3^4+...+3^{2024}\)

\(2C=3C-C=3^{2024}-3\Rightarrow C=\dfrac{3^{2024}-3}{2}\)

\(\Rightarrow2B=2023.3^{2024}-\dfrac{3^{2024}-3}{2}=\)

\(=\dfrac{2.2023.3^{2024}-3^{2024}+3}{2}=\dfrac{4045.3^{2024}+3}{2}\)

\(\Rightarrow B=\dfrac{4045.3^{2024}+3}{4}\)