神马作文网1x2x3+2x3x4+3x4x5+.+n(n+1)(n+2)=?求此类型算数题公式!
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/10/07 18:28:27
1x2x3+2x3x4+3x4x5+.+n(n+1)(n+2)=?求此类型算数题公式!
首先你需要知道3个求和公式：
1+2+3+...+n=n(n+1)/2
1²+2²+3²+...+n²=n(n+1)(2n+1)/6
1³+2³+3³+...+n³=[n(n+1)/2]²
再来看你的这一道题,可以利用上面的3个公式推导出本题的求和公式.
n(n+1)(n+2)=n³+3n²+2n
1×2×3+2×3×4+3×4×5+...+n(n+1)(n+2)
=(1³+2³+3³+...+n³)+3(1²+2²+3²+...+n²)+2(1+2+...+n)
=[n(n+1)/2]²+n(n+1)(2n+1)/2+n(n+1)
=n(n+1)[n(n+1)/4+(2n+1)/2+1]
=n(n+1)[n(n+1)+2(2n+1)+4]/4
=n(n+1)(n²+5n+6)/4
=n(n+1)(n+2)(n+3)/4
本题的求和公式为：
1×2×3+2×3×4+3×4×5+...+n(n+1)(n+2)=n(n+1)(n+2)(n+3)/4
1+2+3+...+n=n(n+1)/2
1²+2²+3²+...+n²=n(n+1)(2n+1)/6
1³+2³+3³+...+n³=[n(n+1)/2]²
再来看你的这一道题,可以利用上面的3个公式推导出本题的求和公式.
n(n+1)(n+2)=n³+3n²+2n
1×2×3+2×3×4+3×4×5+...+n(n+1)(n+2)
=(1³+2³+3³+...+n³)+3(1²+2²+3²+...+n²)+2(1+2+...+n)
=[n(n+1)/2]²+n(n+1)(2n+1)/2+n(n+1)
=n(n+1)[n(n+1)/4+(2n+1)/2+1]
=n(n+1)[n(n+1)+2(2n+1)+4]/4
=n(n+1)(n²+5n+6)/4
=n(n+1)(n+2)(n+3)/4
本题的求和公式为：
1×2×3+2×3×4+3×4×5+...+n(n+1)(n+2)=n(n+1)(n+2)(n+3)/4
1x2x3+2x3x4+3x4x5+4x5x6+...+n(n+1)(n+2)=
1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(nx(n+1)x(n+2)=?
1x2X3+2x3X4+3x4X5+…+7X8X9=?
1x2x3+2x3x4+3x4x5+...+7x8x9=,
求和1x2x3+2x3x4+...+n(n+1)(n+2)
1/1x2x3+1/2x3x4+1/3x4x5
1x2x3+2x3x4+3x4x5+…+8x9x10
1x2x3+2x3x4+3x4x5+.+10x11x12
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+.+1/48x49x50=
1/1x2x3+1/2x3x4+1/3x4x5+.+1/11x12x13=
1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11=
请1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6=