Question

a)1*2*3+2*3*4+...+111*112*113

b)1^3+2^3+3^+...+100^3

Answer 1

Đặt A=1.2.3+2.3.4+...+111.112.113

Ta có:4A=(1.2.3+2.3.4+...+111.112.113).4

          4A=1.2.3.(4-0)+2.3.4.(5-1)+...+111.112.113.(114-110)

          4A=1.2.3.4+2.3.4.5-1.2.3.4+...+111.112.113.114-110.111.112.113

          4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+...+110.111.112.113-110.111.112.113+111.112.113.114

          4A=111.112.113.114

      =)  A= 111.112.113.114/4( chia 4)