A=1.2+2.3+...+199.200

3A = 1.2.3 + 2.3.3 +...+ 199.200.3

3A = 1.2.(3 - 0) + 2.3.(4 - 1) +...+ 199.200. (201 - 198)

3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 199.200.201 - 198.199.200

3A = (1.2.3 + 2.3.4 +...+ 199.200.201) - (0.1.2 + 1.2.3 +...+ 198.199.200)

3A = 199.200.201 - 0.1.2

3A = 199.200.201

A = \(\frac{199.200.201}{3}=2666600\)

Đặt tên biểu thức là A

Ta có : A=1.2+2.3+3.4+..+198.199+199.200

<=> 3A = 1.2.(3 - 0) + 2.3.(4 - 1) + ..... + 199.200.(201 - 98)

<=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + .... + 199.200.201

<=> 3A = 199.200.201

<=> A = 199.200.201 : 3

<=> A = 2 666 600

Vậy A=2 666 600

Đặt A = 1.2 + 2.3 + 3.4 + .... + 199.200

⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 199.200.3

⇒ 3A = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + .... + 199.200.( 201 - 198 )

⇒ 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 199.200.201 - 198.199.200 

⇒ 3A = ( 1.2.3 - 1.2.3 ) + ( 2.3.4 - 2.3.4 ) + .... + ( 198.199.200 - 198.199.200 ) + 199.200.201

⇒ 3A = 199.200.201

⇒ 3A = \(\frac{199.200.201}{3}\)

3A =1.2.3 +2.3.(4-1) +3.4.(5-2) +4.5.(6-3)....+199.200.(201 -198)

    = 1.2.3+2.3.4 -1.2.3 +3.4.5- 2.3.4 + 4.5.6 - 3.4.5 +......+ 199.200.201 -198.199.200

 3A =199.200.201 

A=199.200.67 =254600

S = -5/1.2 + -5/2.3 + -5/3.4 + ... + -5/199.200

S= -5/1 - (-5)/2 +(-5)/2 - (-5)/3+....+ (-5)/199 - (-5)/200

S= -5/1 - (-5)/200

S= -5/1 + 5/200

S= -199/40 

\(S=\frac{-5}{1\cdot2}+\frac{-5}{2\cdot3}+\frac{-5}{3\cdot4}+...+\frac{-5}{199\cdot200}\)

\(S=\frac{-5}{1}-\frac{-5}{2}+\frac{-5}{2}-\frac{-5}{3}+...+\frac{-5}{199}-\frac{-5}{200}\)

\(S=-5+\frac{5}{200}\)

\(S=-\frac{199}{40}\)

Bạn check lại nha, không chắc đâu =.=

http://olm.vn/hoi-dap/question/200195.html

             tick mik nha ! 

Ta có: A=1.2+2.3+...+198.199+199.200 
=>3A=1.2.3+2.3.3+...+198.199.3 
+199.200.3 
=>3A=1.2.3+2.3(4-1)+...+ 
198.199(200-197)+199.200(201-198) 
=>3A=1.2.3+2.3.4-1.2.3+...+198.199.200 
-197.198.199+199.200.201-198.199.200 
=>3A=199.200.201 
=>A=199.200.67

A=39800.67

A=2666600

lấy máy tính mà tính

các bạn troll mình à

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{199\cdot200}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}\)

\(A=1-\frac{1}{200}\)

\(A=\frac{199}{200}\)

\(=1-\frac{1}{200}=\frac{199}{200}\)

\(A=\frac{1}{1.2}+............+\frac{1}{199.200}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-...........+\frac{1}{199}-\frac{1}{200}\)

\(=1-\frac{1}{200}\)

\(=\frac{199}{200}\)

ta có công thức 1.2+2.3+3.4+...+n.(n+1)=\(\frac{n\left(n+1\right)\left(n+2\right)}{3}\)

áp dụng công thức vào bài ta có: 1.2+2.3+3.4+...+2002.2003 = \(\frac{2002.2003.2004}{3}=2678684008\)