求和：1X2X3+2X3X4+3X4X5+...+98X99X100

来源：学生作业帮助网编辑：作业帮时间：2024/04/28 04:28:17

求和：1X2X3+2X3X4+3X4X5+...+98X99X100
求和：1X2X3+2X3X4+3X4X5+...+98X99X100

求和：1X2X3+2X3X4+3X4X5+...+98X99X100
因为(n-1)n(n+1)=n(n²-1)=n³-n
∴原式=2³-2+3³-3+4³-4+……+99³-99
=2³+3³+4³+……+99³-(2+3+4+……+99)
=1³+2³+3³+……+99³-(1³+2+3+……+99)
【这里要知道：连续自然数的立方和等于他们和的平方,即
1³+2³+3³+……+n³=(1+2+3+……+n)²=[n(n+1)/2]²】
=[99×(99+1)/2]²-99×(99+1)/2
=99×100/2×(99×100/2-1)
=99×50×(99×50-1)
=24497550
【本题总结】
1×2×3+2×3×4+……+(n-1)n(n+1)
=1³+2³+3³+……+n³-(1+2+3+……+n)
=[n(n+1)/2]²-n(n+1)/2
=[n(n+1)/2][n(n+1)/2-1]
=1/4×{n(n+1)[n(n+1)-2]}

求和：1X2X3+2X3X4+3X4X5+...+98X99X100 1x2x3+2x3x4+3x4x5+…+8x9x10 1x2x3+2x3x4+3x4x5+.+10x11x12 1x2x3+2x3x4+3x4x5+...+7x8x9=, 1x2X3+2x3X4+3x4X5+…+7X8X9=? 1x2x3 2x3x4 3x4x5 .10x11x12,怎么算 1x2=1|3(1x2x3-0x1x2) 2x3=1|3(2x3x4-1x2x3) 3x4=1|3(3x4x5-2x3x4)由此推断1x2x3+2x3x4+3x4x5.7x8x9=? 1x2=1/3x(1x2x3-0x1x2)2x3=1/3x(2x3x4-1x2x3)3x4=1/3x(3x4x5-2x3x4)求1x2x3+2x3x4+3x4x5+...+7x8x9=? 1/1x2x3+1/2x3x4+1/3x4x5+.+1/n(n+1)(n+2) 2/1x2x3+2/2x3x4+2/3x4x5+2/4x5x6+...+2/98x99x100= 1/1x2x3+1/2x3x4+1/3x4x5+.+1/8x9x10 求简算请1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6= 1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100= 1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=? 1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11= 1/1x2x3+1/2x3x4+1/3x4x5+.1/98x99x100=要有中间过程 1/1x2x3+1/2x3x4+1/3x4x5+.+1/11x12x13= 1x2x3+2x3x4+3x4x5+4x5x6+...+n(n+1)(n+2)=