求和1x2x3+2x3x4+...+n(n+1)(n+2)

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 10:45:32

求和1x2x3+2x3x4+...+n(n+1)(n+2)
求和1x2x3+2x3x4+...+n(n+1)(n+2)

求和1x2x3+2x3x4+...+n(n+1)(n+2)
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.
思考题:
nn=n(n+1)-n
你能用类似方法求出sum(nn)吗?sum表示从i=1到n求和.
那么sum(nnn)呢?

求和1x2x3+2x3x4+...+n(n+1)(n+2) 求和Sn=1x2x3+2x3x4+……+n(n+1)(n+2) 求和：1X2X3+2X3X4+3X4X5+...+98X99X100 Sn=1/(1x2x3)+1/(2x3x4)+...+1/(n(n+1)(n+2))求和,不要数学归纳法 1X2X3+2X3X4+.+n(n+1)(n+2) 1x2x3+2x3x4+.+n(n+1)(n+2)=? 1x2x3+2x3x4+.+nx(n+1)(n+2)=? 1x2x3+2x3x4+…+n(n+1) 1x2x3+2x3x4+...+nxx=? 1/1x2x3+1/2x3x4+1/3x4x5+.+1/n(n+1)(n+2) 1x2x3+2x3x4+3x4x5+4x5x6+...+n(n+1)(n+2)= 1X2X3+2X3X4+...+n(n+1)(n+2)等于多少呢 1X2X3+2X3X4+3X4+.+nx(n+1)(n+2)= 1/1x2x3+1/2x3x4+.+1/98x99x100 . 1/1X2X3+1/2X3x4+…+1/48X49X50 1x2x3+2x3x4+3x4x5+…+8x9x10 1x2x3+2x3x4+3x4x5+.+10x11x12 1x2x3+2x3x4+3x4x5+...+7x8x9=,