Đặt \(A=1.2.3+2.3.4+3.4.5+...+99.100.101\)

\(\Rightarrow4A=1.2.3.4+2.3.4.4+...+99.100.101.4\)

\(=1.2.3\left(4-0\right)+2.3.4\left(5-1\right)+...+99.100.101\left(102-98\right)\)

\(=\left(1.2.3.4+2.3.4.5+...+99.100+101.102\right)-\left(0.1.2.3+1.2.3.4+...+98.99.100.101\right)\)

\(=99.100.101.102-0.1.2.3\)

\(=101989800\)

\(\Rightarrow A=101989800:4=25497450\)

Vậy \(A=25497450.\)

Đặt A = 1.2.3 + 2.3.4 + ... + 99.100.101

=> 4A = 1.2.3.4 + 2.3.4.(5-1) + ... + 99.100.101.(102-98)

=> 4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + ... + 99.100.101.102 - 98.99.100.101

=> 4A = 99.100.101.102

=> 4A = 101989800

=> A = 25497450

1.2.3 = 1/4 . (1.2.3.4 - 0.1.2.3)

2.3.4 = 1/4 . (2.3.4.5 - 1.2.3.4)

3.4.5 = 1/4 . (3.4.5.6 - 2.3.4.5)

.................

99.100.101 = 1/4 . (99.100.101.102 - 98.99.100.101)

C = 1.2.3+2.3.4+3.4.5+.........+99.100.101

C= 1/4 . (99.100.101.102 - 98.99.100.101)

CHUC BN HOK GIỎI!

25497450

Đặt A=1/1.2.3+1/2.3.4+...+1/99.100.101 

2A=2/1.2.3+2/2.3.4+...2/99.100.101

2A=3-1/1.2.3+4-2/2.3.4+...+101-99/99.100.101

2A=3/1.2.3-1/1.2.3+4/2.3.4-2/2.3.4+...+101/99.100.101-99/99.100.101

2A=1/1.2-1/2.3+1/2.3-1/3.4+...+1/99.100-1/100.101

2A=1/2-1/10100

\(A=1.2.3+2.3.4+...+99.100.101\)

\(\Rightarrow4A=1.2.3.4+2.3.4\left(5-1\right)+...+99.100.101.\left(102-98\right)\)

\(=1.2.3.4+2.3.4.5-1.2.3.4+...+99.100.101.102-98.99.100.101\)

\(=99.100.101.102\)

\(\Rightarrow A=\dfrac{99.100.101.102}{4}=99.25.101.102\)

Vậy...

mình ko biết 

  A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 99.100.101

4A = 4.(1.2.3 + 2.3.4 + 3.4.5 + ... + 99.100.101)

     = 1.2.3.(4-0) + 2.3.4.(5-1) + 3.4.5.(6-2) + ... + 99.100.101.(102-98)

     = 1.2.3.4 - 1.2.3.4 + 2.3.4.5 - 2.3.4.5 + 3.4.5.6 - 3.4.5.6 + ... + 98.99.100.101 - 98.99.100.101 + 99.100.101.102

4A = 99.100.101.102

  A = 99.100.101.102 : 4 

  A = 25497450