Lời giải :

Đặt S=1.2+2.3+3.4+4.5+…+99.100+100.101

3S=1.2.3+2.3.3+3.4.3+4.5.3+…+99.100.3+100.101.3

=1.2(3−0)+2.3(4−1)+3.4(5−2)+4.5(6−3)+…+99.100(101−98)+100.101(102−99)

=0.1.2-1.2.3+1.2.3-2.3.4+...+99.100.101-100.101.102

=100.101.102

S=100.101.34=343400

1.Tính 

a) Ta có: 

  A=(1-1/2²).(1-1/3²)...(1-1/100²)

=>A=3/2².8/3².....9999/100²

=>A=(1.3/2.2).(2.4/3.3).....(99.101/100.100)

=>A=(1.2.3.....99/2.3.4.....100).(3.4.5.....101/2.3.4.....100)

=>A=1/100.101/2

=>A=101/200

b) Ta có: 

  B=-1/1.2-1/2.3-1/3.4-...-1/100.101

=>B=-(1/1.2+1/2.3+1/3.4+...+1/100.101)

=>B=-(1-1/2+1/2-1/3+1/3-1/4+...+1/100-1/101)

=>B=-(1-1/101)

=>B=-100/101

 c) Ta có:

 C=1.2+2.3+3.4+...+100.101

       =>3C=1.2.3+2.3.3+3.4.3+...+100.101.3

       =>3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+100.101.(102-99)

       =>3C=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+...+100.101.102

       =>3C=100.101.102

       =>3C=1030200

       =>C=343400

Chúc bạn hok tốt nhé >:)!!!!!

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

Nhớ **** cho mjk với nhak!!!!!

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

Nhớ **** cko mjk nhak!!

A = 1.2 + 2.3 + 3.4 + ...... + 100.101

3A = 1.2.3 + 2.3.3 + 3.4.3 + ...... + 100.101.3

3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ..... + 100.101.(102 - 99)

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ...... + 100.101.102 - 99.100.101

3A = 100.101.102

A = 100.101.34

A = 343400

ĐẶT S = 1.2 + 2.3 +3.4 +........ + 100.101 

3S = 1 . 2 .3 + 2 . 3 . 3+ 3.4.3 + ....... + 99 . 100 . 3

3S= 1 . 2 . 3 + 2. 3 . ( 4-1 ) + .........  + 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

3S = 3 .33 . 100 . 101

S= 33 . 100 . 101 = 333300

Đặt A = 1.2+2.3+3.4+...+100.101

3A = 1.2.3+2.3.3+3.4.3+...+100.101.3

3A= 1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+100.101.(102-99)

3A= 1.2.3-0.1.2+2.3.4-1.2.3+...+100.101.102-99.100.101

3A= (1.2.3-1.2.3)+(2.3.4-2.3.4)+...+(99.100.101-99.100.101)+(100.101.102-0.1.2)

3A= 0+0+...+0+(100.101.102-0.1.2)

3A= 100.101.102-0.1.2

3A= 100.101.102

A= (100.101.102):3

A= 1030200:3

A= 343400

Tớ ngắn gọn hơn nè

Ta có: \(A=1.2+2.3+3.4+...+100.101\)

\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+100.101.3\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+100.101\left(102-99\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+100.101.102-99.100.101\)

\(\Rightarrow3A=\left(1.2.3-1.2.3\right)+...+\left(99.100.101-99.100.101\right)+100.101.102\)

\(\Rightarrow3A=\) \(100.101.102\)

\(\Rightarrow A=\dfrac{100.101.102}{3}=343400\)

Vậy \(A=343400.\)

A = 1.2+2.3+3.4+.....+100.101

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

câu này trên gg có r` bn!! bn lên tra nhé! mk k lm lại nx! Tiến Đạt

ps: gg là google

A = 1.2 + 2.3 + 3.4 + 4.5 + ... + 99.100 + 100.101

3.A = 1.2.3 + 2.3.3 +3.4.3 + ... + 100.101.3

3A= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 100.101.(102 - 99)

3A = 1.2.3 + 2.3.4 - 1.2.3 + 2.3.4 -3.4.5 + ... +99.100.101 -100.101.102

3A = 99.100.101

A = 99.100.101 : 3

A = 33.100.101

Vậy A = 33. 100 .101 (Tự tính)

A=1.2+2.3+3.4+.....+99.100+100.101

333300

Áp dụng \(\frac{1}{a.\left(a+1\right)}=\frac{1}{a}-\frac{1}{a+1}\)

Ta có \(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{100.101}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

1/1.2+1/2.3+1/3.4+.....+1/100/101

=1-1/2+1/2-1/3+1/3-1/4+.....+1/100-1/101

=1-1/101

=100/101

mình không mua được vip

các bạn giúp mk với

A = 1.2 + 2.3 + 3.4 + ... + 99.100 + 100.101

⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3 + 100.101.3

= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98) + 100.101.(102 - 99)

= 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 + ... - 98.99.100 + 99.100.101 - 99.100.101 + 100.101.102

= 100.101.102

= 1030200

⇒ A = 1030200 : 3

= 343400