Question

tính tổng M=1.2+2.3+3.4+...+199.200

Answer 1

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