1x2x3+2x3x4+…+n(n+1)

1x2x3+2x3x4+…+n(n+1) 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)=? 求和Sn=1x2x3+2x3x4+……+n(n+1)(n+2) 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)= 1.1X2=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). 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)=___________ 1/1X2X3+1/2X3x4+…+1/48X49X50 1x2x3+2x3x4+3x4x5+…+8x9x10 1x2X3+2x3X4+3x4X5+…+7X8X9=?