求数列1*2*3,2*3*4,4*5*6,…n(n+1)(n+2),…的Sn
问题描述:
求数列1*2*3,2*3*4,4*5*6,…n(n+1)(n+2),…的Sn
答
1*2*3+2*3*4+…+n(n+1)(n+2)=2(2^2-1)+3(3^2-1)+…+〔(n+1))〔(n+1)^2-1〕=2^3-2+3^3-3+…+(n+1)^3-(n+1)=〔2^3+3^3+…+(n+1)^3〕-(2+3+4…+n+1)=〔(n+1)(n+2)/2〕〔(n+1)(n+2)/2-1〕