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

Đặt S= 1.2 + 2.3 + 3.4 + ...+ 99.100
 3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101  3S = 3.33.100.101 
 S=33.100.101= 333300

3A=1.2.3+2.3.(4-1)+.............+98.99.(100-97)+99.100.(101-98)

3A=1.2.3+2.3.4-1.2.3+...........+98.99.100-97.98.99+99.100.101-98.99.100

3A=99.100.101

A=99.100.101:3

A=333300

Ta có : 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 98.99.3 + 99.100.3

=> 3A = 1.2.( 3 - 0 ) + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ..... + 98.99.( 100 - 97 ) + 99.100.( 101 - 98 )

=> 3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 98.99.100 - 97.98.99 + 99.100.101 - 98.99.100

=> 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 + ..... + 98.99.100 )

=> 3A = 99.100.101 - 0.1.2

=> 3A = 99.100.101

=> A = 33.100.101

=> A = 333300

\(\text{Ta có: A = 1.2+2.3+3.4+4.5+...+99.100 }\)

=>  3A = 3.(1.2+2.3+3.4+4.5+...+99.100)

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

=>  3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + .......... + 99.100.101

=>  3A = 99.100.101

\(\Rightarrow A=\frac{99.100.101}{3}=333300\)

k mình nếu đúng OK

Dãy số trên có số lượng các số là :

       (99,100 - 1,2) : 1,1 + 1 = 90 (số)

A = (1,2 + 99,100) x 90 : 2 = 4513,5

             Đáp số : A = 4513,5.

Đặt A= 1.2 + 2.3 + 3.4 + ...+ 99.100
 3A = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3A= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3A= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3A = 99.100.101  3S = 3.33.100.101 
 A=33.100.101= 333300

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

3A = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3

3A= 1.2.3+2.3﴾4‐1﴿+3.4﴾5‐2﴿+...+98.99﴾100‐97﴿+99.100﴾101‐98﴿  

3A= 1.2.3+2.3.4‐1.2.3+3.4.5‐2.3.4+...‐97.98.99+99.100.101‐98.99.100

3A = 99.100.101 3S = 3.33.100.101

A=33.100.101= 333300

1.2 là 1 x 1 hay 1,2 vậy

Áp dụng công thức ta có :

\(A=1.2+2.3+3.4+...+99.100=\frac{99.100.101}{3}=333300\)

A=1.2+2.3+3.4+4.5+.....+98.99+99.100 Rút gọn đi ta còn:

A=1+100

=>A=101

Ta có : A = 1.2 + 2.3 + 3.4 + ....... + 99.100

=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 99.100.101

=> 3A = 99.100.101

=> A = 99.100.101/3

=> A = 333300