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

Đặt A = 1.2 + 2.3 + 3.4 + ...+99.100

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

=> 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 + 4.5.6 - 3.4.5 + ... + 99.100.101-98.99.100

=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 - 3.4.5 + ... + 99.100.101

=> 3A = 99.100.101

=> 3A = 999900

=> A = 999900 : 3

=> A = 333300

 Vậy A = 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

1.2+2.3+3.4+....+99.100

=(99.100.101-0.1.2)÷3

=333300

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

= 99.100.101

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

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

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

3A = 1.2.3 + 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

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

=>3A=1.2.3+2.3.3+3.3.4+....+99.100.3

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

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

=99.100.101-0

=999900

=>A=999900:3=333300

số số hạng : (99,100 -1.2) : 1.1 +1=90 số 

Tổng: (99.100 +1.2) x 90 : 2= 4513 ,5

\(A=1.2+2.3+3.4+....+99.100\\ 3.A=1.2.3+2.3.3+....+99.100.3\)

\(3.A=1.2.3+2.3.\left(4-1\right)+....+99.100\left(101-98\right)\\ 3.A=1.2.3+.....+99.100.101-98.99.100\)

\(3.A=99.100.101\\ A=33.100.101=333300\)

A=1/1-1/2+1/2-1/3+1/3-1/4+...............+1/99-1/100

A=1/1-1/100

A=100/100-1/100

A=99/100

Mk ko chép đề bài

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}.+.....+\frac{1}{99}-\frac{1}{100}\)

\(A=1-\frac{1}{100}\)

\(A==\frac{99}{100}\)

S=1.2+2.3+3.4+...+99.100

3S=1.2.3+2.3.3+3.4.3+...+99.100.3

3S=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)

3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100

3S=99.100.101

S=33.100.101

S=3333.100

S=333300

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

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}\)

\(=\frac{2}{1.2}-\frac{1}{1.2}+\frac{3}{2.3}-\frac{2}{2.3}+....+\frac{100}{99.100}-\frac{99}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)

1-1/2+1/2-1/3+1/3-1/4+1/4-..........+1/99-1/100=1-1/100=99/100