1X2X1/3+2X3X1/4+3X4X1/5+4X5X1/6+5X6X1/7+6X7X1/8+7X8X1/9+8X9X1/10+9X10X1/11求和？

1X2X1\/3+2X3X1\/4+3X4X1\/5+4X5X1\/6+5X6X1\/7+6X7X1\/8+7X8X1\/9+8X9X1\/...
因为an=n*(n-1)\/n+1 所以每个数可以看成2\/3+（1+2\/4）+（2+2\/5）+（3+2\/6）...+（8+2\/11）= 1+2+3...+8+2\/3+2\/4+2\/5...+2\/11=36+2*（1\/3+1\/4+1\/5+...1\/11）因为后面的那个是一个发散数列，好像没有求和公式，所以只能同分计算，当然可以把简单的算出来，...

1X2X1\/3+2X3X1\/4+3X4X1\/5+4X5X1\/6+5X6X1\/7+6X7X1\/8+7X8X1\/9+8X9X1\/...
所以每个数可以看成2\/3+（1+2\/4）+（2+2\/5）+（3+2\/6）...+（8+2\/11）= 1+2+3...+8+2\/3+2\/4+2\/5...+2\/11=36+2*（1\/3+1\/4+1\/5+...1\/11）因为后面的那个是一个发散数列，好像没有求和公式，所以只能同分计算，当然可以把简单的算出来，剩下36+2*（1\/4+1\/5+...

1×2×3×4分之一+2×3×4×5分之一+……+7×8×9乘10分之一。 十分 ...
第一步列式子:1x2x3x1\/4+2x3x4x1\/5+3x4x5x1\/6+4x5x6x1\/7+5x6x7x1\/8+6x7x8x1\/9+7x8x9x1\/10 第二步能化简的分数进行化简:3x1\/2+2x3x4x1\/5+10+4x5x6x1\/7+5x3x7x1\/4+2x7x8x1\/3+7x4x9x1\/5(简要说明下:那个整数10是通过"3x4x5"得到的60,在进行和1\/6化简得到的)计算...

...1x2\/1+2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1 过程写清楚._百...
是不是：1x1\/2+2x1\/3+3x1\/4+4x1\/5+5x1\/6+6x1\/7+7x1\/8+8x1\/9 ＝1\/2+2\/3+3\/4+4\/5+5\/6+6\/7+7\/8+8\/9 =33\/12+4\/5+6\/7+7\/8+8\/9 =22\/8+7\/8+4\/5+6\/7+8\/9 =29\/8+4\/5+6\/7+8\/9 =177\/40+6\/7+8\/9 1479\/280+8\/9 =14511\/1520 ...

简算题:1x2\/1+2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1
是不是：1x1\/2+2x1\/3+3x1\/4+4x1\/5+5x1\/6+6x1\/7+7x1\/8+8x1\/9 ＝1\/2+2\/3+3\/4+4\/5+5\/6+6\/7+7\/8+8\/9 =33\/12+4\/5+6\/7+7\/8+8\/9 =22\/8+7\/8+4\/5+6\/7+8\/9 =29\/8+4\/5+6\/7+8\/9 =177\/40+6\/7+8\/9 1479\/280+8\/9 =14511\/1520 ...

六年级奥数计算题1x2x1\/3+2x3x1\/4+3x4x1\/5+---98x99x1\/100=?
=n-n\/n+2 =n-(n+2-2)\/(n+2)=(n-1)+2\/n+2 ∴1x2x1\/3+2x3x1\/4+3x4x1\/5+---98x99x1\/100 =1x2\/3+2x3\/4+3x4\/5+...+98x99\/100 =(1-1)+2\/3+(2-1)+2\/4+(3-1)+2\/5+...+(98-1)+2\/100 =(0+1+2+...+97)+2(1\/3+1\/4+1\/5+...+1\/100)=(...

2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1+9x10\/1+10x11\/1=
解:①2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1+9x10\/1+10x11\/1 =6+12+20+30+42+56+72+90+110 =(6+12+72)+(20+30+90+110)+(42+56)=90+250+98 =438 ②如果楼主原意这样，那么解法不同:1\/2x3+1\/3x4+1\/4x5+1\/5x6+1\/6x7+1\/7x8+1\/8x9+1\/9x10+1\/1...

1×2+2×3+3×4+4×5+5×6+6×7+7×8…+10×11=?
1×2+2×3+3×4+4×5+5×6+6×7+7×8…+10×11 =1×(1+1)+2×(2+1)+…+10×(10+1)=1^2+1+2^2+2+...+10^2+10 =(1^2+2^2+...+10^2)+(1+2+...+10)=10*(10+1)(2*10+1)\/6+(1+10)*10\/2 = 385+55 = 440 ...

2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1+9x10\/1+10x11\/1=
解：①2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1+9x10\/1+10x11\/1 =6+12+20+30+42+56+72+90+110 =(6+12+72)+(20+30+90+110)+(42+56)=90+250+98 =438 ②如果楼主原意这样，那么解法不同：1\/2x3+1\/3x4+1\/4x5+1\/5x6+1\/6x7+1\/7x8+1\/8x9+1\/9x10+1\/...

1x2\/1+2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1+9x10\/1
1x2\/1+2x3\/1+3x4\/1+4x5\/1+5x6\/1+6x7\/1+7x8\/1+8x9\/1+9x10\/1 ＝1\/2+1\/6+1\/12+1\/20+1\/30+1\/42+1\/56+1\/72+1\/90 =(1-1\/2)+(1\/2-1\/3)+……+(1\/8-1\/9)+(1\/9-1\/10)=1-1\/10 =9\/10