Question

1*2+2*3+3*4+...+199*200

 

Answer 1

Đặt A = 1.2 + 2.3 + 3.4 + ...... + 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

Answer 2

Ta có : 
A = 1.2 + 2.3 + 3.4 + ... + 198.199 + 199.200 
= 1.(1 + 1) + 2.(2 + 1) + 3.(3 + 1) + ... + 198(198 + 1) + 199(199 + 1) 
= (1^2 + 1) + (2^2 + 2) + (3^2 + 3) + ... + (198^2 + 198) + (199^2 + 199) 
= (1 + 2 + 3 + 4....+ 198 + 199) + (1^2 + 2^2 + 3^2 + ...+ 198^2 + 199^2) 
* Dễ chứng minh : 
....1 + 2 + 3 +...+ n = n(n + 1)/2 
.... 1^2 + 2^2 +...+ n^2 = [n(n + 1)(2n + 1)]/6 
Suy ra : A = [199.(199 + 1)]/2 + [199.(199 + 1)(2.199 + 1)]/6 = 2666600 

Answer 3

Hoặc

 Ta co: 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

Answer 4

đặt tên biểu thức là A

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

      A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + ... + 198.199.3 + 199.200.3

    A . 3 = 1.2.3 + 2.3.(4-1) + 3.4.(5-2)  + ... + 198 . 199. ( 200-197 ) + 199.200 . (201 - 198 )

  A . 3   = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 198.199.200 - 197.198.199 + 199.200.201 - 198.199.200

 A . 3 = 199.200.201

    A = 199.200.201:3

A = 2666600 

Answer 5

đặt tên biểu thức là A

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

      A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + ... + 198.199.3 + 199.200.3

    A . 3 = 1.2.3 + 2.3.(4-1) + 3.4.(5-2)  + ... + 198 . 199. ( 200-197 ) + 199.200 . (201 - 198 )

  A . 3   = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 198.199.200 - 197.198.199 + 199.200.201 - 198.199.200

 A . 3 = 199.200.201

    A = 199.200.201:3

A = 2666600 

Answer 6

Hoặc

 Ta co: 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

Answer 7

Ta có : 
A = 1.2 + 2.3 + 3.4 + ... + 198.199 + 199.200 
= 1.(1 + 1) + 2.(2 + 1) + 3.(3 + 1) + ... + 198(198 + 1) + 199(199 + 1) 
= (1^2 + 1) + (2^2 + 2) + (3^2 + 3) + ... + (198^2 + 198) + (199^2 + 199) 
= (1 + 2 + 3 + 4....+ 198 + 199) + (1^2 + 2^2 + 3^2 + ...+ 198^2 + 199^2) 
* Dễ chứng minh : 
....1 + 2 + 3 +...+ n = n(n + 1)/2 
.... 1^2 + 2^2 +...+ n^2 = [n(n + 1)(2n + 1)]/6 
Suy ra : A = [199.(199 + 1)]/2 + [199.(199 + 1)(2.199 + 1)]/6 = 2666600