\(a,A=1\cdot2+2\cdot3+...+98\cdot99\\ 3A=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+98\cdot99\cdot3\\ 3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\left(5-2\right)+...+98\cdot99\left(100-97\right)\\ 3A=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4-2\cdot3\cdot4+3\cdot4\cdot5-...-97\cdot98\cdot99+98\cdot99\cdot100\\ 3A=98\cdot99\cdot100=970200\\ A=323400\)

\(b,B=1^2+2^2+3^3+...+98^2\\ B=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+98\left(99-1\right)\\ B=\left(1\cdot2+2\cdot3+3\cdot4+...+98\cdot99\right)-\left(1+2+...+98\right)\\ B=323400-\left[\left(98+1\right)\left(98-1+1\right):2\right]\\ B=323400-4851=318549\\ c,C=1\cdot99+2\left(99-1\right)+3\left(99-2\right)+...+98\left(99-97\right)+99\left(99-98\right)\\ C=1\cdot99+2\cdot99-1\cdot2+3\cdot99-2\cdot3+...+98\cdot99-97\cdot98+99\cdot99-98\cdot99\\ C=99\left(1+2+...+99\right)-\left(1\cdot2+2\cdot3+...+98\cdot99\right)\\ C=99\left[\left(99+1\right)\left(99-1+1\right):2\right]-323400\\ C=490050-323400=166650\)

https://hoc24.vn/cau-hoi/a-tinh-tong-a1223349899b-su-dung-ket-qua-cau-a-tinh-b122232972982c-su-dung-ket-qua-cau-a-tinh-c1992983979829.2030286199021

:vv hỏi hoài z?

Mình làm mẫu 1 bài nha !

Có : 12A = 1.5.12+5.9.12+....+101.105.12

= 1.5.12+5.9.(13-1)+.....+101.105.(109-97)

= 1.5.12+5.9.13-1.5.9+.....+101.105.109-97.101.105

= 1.5.12-1.5.9+101.105.109

= 1155960

=> A = 1155960 : 12 = 96330

Tk mk nha

Có : 4D = 1.2.3.4+2.3.4.4+....+98.99.100.4

= 1.2.3.4+2.3.4.(5-1)+.....+98.99.100.(101-97)

= 1.2.3.4+2.3.4.5-1.2.3.4+......+98.99.100.101-97.98.99.100

= 98.99.100.101

=> D = 98.99.100.101/4 = 24497550

a ta co ;

13 -12 +11+10-9+8-7-6+5-4+3+2-1

=13-(12-11-10+9) +(8-7-6+5) -(4-3-2+1)

= 13 -0+0 -0

=13

câu a = 13 còn câu b thì để tuần sau nhé

13-12+11+10-9+8-7-6+5-4+3+2-1

=11+11+10-9+8-7-6+5-4+3+2-1

=    22  +  1  + 1  - 11  - 7  + 1

=          23     +1  -11-7+1

=                24 -11-7+1

=                    13-8

=                        5

Đặt A= 1.2+2.3 +.......+99.100

3A= 1.2.3+2.3.4+3.4.3 +......+ 99.100.3

3A= 1.2. (3 - 0) + 2.3.(4 - 1) +3.4. (5 - 2)....... . 99.100. (101 - 98)

3A = (1.2.3 + 2.3.4 + 3.4.5 +...... + 99.100.101) - (0.1.2 + 1.2.3 + 2.3.4 +.......+ 98.99.100)

3A = 99.100.101 - 0.1.2

3A = 999900 - 0

3A= 999900

A= 999900 : 3

A = 333300

Đặt A= 1.2+2.3 +.......+99.100

3A= 1.2.3+2.3.4+3.4.3 +......+ 99.100.3

3A= 1.2. (3 - 0) + 2.3.(4 - 1) +3.4. (5 - 2)....... . 99.100. (101 - 98)

3A = (1.2.3 + 2.3.4 + 3.4.5 +...... + 99.100.101) - (0.1.2 + 1.2.3 + 2.3.4 +.......+ 98.99.100)

3A = 99.100.101 - 0.1.2

3A = 999900 - 0

3A= 999900

A= 999900 : 3

A = 333300

nguồn:câu hỏi tương tự

Gọi A là biểu thức ta có: 
A = 1.2+2.3+3.4+......+99.100 
Gấp A lên 3 lần ta có: 
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3 
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98) 
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 
A . 3 = 99.100.101 
A = 99.100.101 : 3 
A = 33.100.101 
A = 333 300

33300

333300

A = 1.2 + 2.3 + 3.4 + .. + 99.100

<=> 3A = 1.2.3 + 2.3.3 + 3.4.3 +...+ 99.100.3

            = 1.2.3 + 2.3.(4-1) + 3.4.( 5 -2) +...+ 99.100.(101-98)

            = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 + ..- 98.99.100 + 99.100.101

            = 999900

<=> A = 999900 : 3 = 333300

A=1.2+2.3+3.4+...+99.100

3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)

3A=1.2.3+2.3.4+3.4.5+...+98.99.100+99.100.101 - 0.1.2-1.2.3-2.3.4-3.4.5-...-98.99.100

3A=99.100.101-0.1.2

3A=999900-0

3A=999900

A=999900:3

A=333300

đơn giản