1X2X3+2X3X4+.+n(n+1)(n+2)

来源：学生作业帮助网编辑：作业帮时间：2024/05/09 05:29:35

1X2X3+2X3X4+.+n(n+1)(n+2)
1X2X3+2X3X4+.+n(n+1)(n+2)

1X2X3+2X3X4+.+n(n+1)(n+2)
1*2*3+2*3*4+.+n*(n+1)(n+2)
=1/4[(1*2*3*4-0*1*2*3)+(2*3*4*5-1*2*3*4)+.+
n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)]
=1/4*n(n+1)(n+2)(n+3)

n(n+1)(n+2)=n^3+3n^2+2n
原式=(1^3+2^3+……+n^3)+3*(1^2+2^2+……+n^2)+
2*(1+2+……+n)
=1/4*n^2*(n+1)^2+1/2*n(n+1)(2n+1)+n(n+1)
再化简一下就行

n(n+1)(n+2) = 1/4(n+3 - (n-1))*n(n+1)(n+2)
= 1/4n(n+1)(n+2)(n+3) - 1/4(n-1)(n)(n+1)(n+2)
所以，原式=1/4*[1*2*3*4 - 0 + 2*3*4*5 - 1*2*3*4 +...+
n(n+1)(n+2)(n+3) - (n-1)(n)(n+1)(n+2)]
=1/4n(n+1)(n+2)(n+3)

1X2X3+2X3X4+.+n(n+1)(n+2) 1x2x3+2x3x4+.+n(n+1)(n+2)=? 求和1x2x3+2x3x4+...+n(n+1)(n+2) 1x2x3+2x3x4+.+nx(n+1)(n+2)=? 1x2x3+2x3x4+…+n(n+1) 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)等于多少呢求和Sn=1x2x3+2x3x4+……+n(n+1)(n+2) 1X2X3+2X3X4+3X4+.+nx(n+1)(n+2)= Sn=1/(1x2x3)+1/(2x3x4)+...+1/(n(n+1)(n+2))求和,不要数学归纳法求证1/1X2X3+1/2X3X4+...+1/n(n+1)(n+2)=n(n+3)/4(n+1)(n+2) 用数学归纳法证明 1x2x3+2x3x4+3x4x5+...+n(n+1)(n+2)=1/4(n+1)(n+2)(n+3)) 1x2=(1/3)(1x2x3-0x1x2) 3x4=(1/3)(3x4x5-2x3x4) 问1x2x3+2x3x4+.+n(n+1)(n+2)=___________ 1x2x3+2x3x4+...+nxx=? 1x2+2x3+3x4+...+n(n+1)=?1x2x3+2x3x4+3x4x5+...+n(n+1)(n+2)=? 1x2+2x3+3x4+...+nx(n+1)= 1x2x3＋2x3x4＋...＋n(n＋1)(n＋2)= 只写答案 1.1X2=1/3(1X2X3-0X1X2)2X3=1/3(2X3X4-1X2X3)3X4=1/3(3X4X5-2X3X4)将这三个等式的两边相加,可以得到1X2+2X3+3X4=(1/3)X3X4X5请计算：1X2X3+2X3X4+…n(n+1)(n+2).