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 = 99x100x101 A = 333300

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 = 99x100x101
A = 333300

\(B=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2022.2023}\)

\(B=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\)

\(B=\dfrac{1}{2}-\dfrac{1}{2023}=\dfrac{2021}{4046}\)

Ta có: \(D=\frac{1}{1\times2}+\frac{1}{2\times3}+\cdots+\frac{1}{2022\times2023}\)

\(=1-\frac12+\frac12-\frac13+\cdots+\frac{1}{2022}-\frac{1}{2023}\)

\(=1-\frac{1}{2023}=\frac{2022}{2023}\)

A 

phân tích : 

= 2 + 6 + 12 + 20 + 30 ... + 2450

quy luật : 2 số liền nhau hơn kém nhau là các số chẵn liên tiếp :
   6 - 2 = 4 ; 12 - 6 = 6 ; 20 - 12 = 8

và bây giờ dùng tính chất dãy số để tính 

nhé !

A×3=1.2.3+2.3.3+3.4.3+.......+49.50.3

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

A×3=1.2.3-1.2.0+2.3.4-2.3.1+........+49.50.51-49.50.48

Ta thấy ngoài số 49.50.51 thì các số còn lại đều bị giản ước như 1.2.3 với 2.3.1;....nên 

A×3=49.50.51

A×3=124950

A=124950:3

A=41650.

Vậy A=41650.

Ax3= 1x2x3 + 2x3x3+.....+29x30x3
lấy B= 1x2x3+ 2x3x4+......+29x30x31
B- Ax3= 0 + 1x2x3+ 2x3x4+ 28x29x30= B- 29x30x31. Suy ra Ax3= 29x30x31

Ax3= 1x2x3 + 2x3x3+.....+29x30x3 lấy B= 1x2x3+ 2x3x4+......+29x30x31 B- Ax3= 0 + 1x2x3+ 2x3x4+ 28x29x30= B- 29x30x31. Suy ra Ax3= 29x30x31

A=1x2+2x3+3x4+4x5+......+99x100+100x101

3A=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+4x5x(6-3)+...+99x100x(101-98)+100x101x(102-99)

3A=1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+4x5x6-3x4x5+...+99x100x101-98x99x100+100x101x102-99x100x101

3A=(1x2x3+2x3x4+3x4x5+4x5x6+...+99x100x101+100x101x102)-(0x1x2+1x2x3+2x3x4+3x4x5+...+98x99x100+99x100x101)

3A=100x101x102

A=100x101x102:3

A=343400

A = 1x2 + 2x3 + 3x4 + 4x5 + ... + 99x100 + 100x101

3A = 1x2x(3-0) + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98) + 100x101x(102-99)

3A = 1x2x3 - 0x1x2 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100 + 100x101x102 - 99x100x101

3A = 100x101x102 - 0x1x2

3A = 100x101x102

A = 100x101x34

A = 343400

544448/468484+464684

21 + 34 + 36 - 12

=  (34 + 36) + (21 - 12)

= 70 + 9

 = 79

Chúc bn học tốt!

Mik ghi nhầm!