求和1x2x3+2x3x4+...+n(n+1)(n+2)
问题描述:
求和1x2x3+2x3x4+...+n(n+1)(n+2)
答
最简方法:拆项法n(n+1)(n+2)=1/4*[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)]...2x3x4=1/4*[2x3x4*5-1*2x3x4]1x2x3=1/4*[1x2x3*4-0*1x2x3]求知即得1x2x3+2x3x4+...+n(n+1)(n+2)=1/4*[n(n+1)(n+2)(n+3)知此一种方法就够了....