1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11

1. 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11

1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11
=10×（10+1）×（10+2）÷3
=10×11×12÷3
=110×12÷3
=1320÷3
=440

2. 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9=

1x2 + 2x3 + 3x4 + ...... + n(n+1) = 1/3 * n(n+1)(n+2)

1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9
= 1/3 * 8 * 9 * 10
= 240

3. (1x2x3x4x5x6)÷(7x8x9x10)？

因为2×5=10可以约掉，
3×4×6=3×4×3×2=（3×3）×（4×2）=9×8也可以约掉
最后是1/7

4. 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11

1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11
  =10×（10+1）×（10+2）÷3
  =10×11×12÷3
  =110×12÷3
  =1320÷3
  =440

5. 10×10-9×9十8x8-7x7十6x6-5x5十4x4-3x3十2x2-1x1

10×10-9×9十8x8-7x7十6x6-5x5十4x4-3x3十2x2-1x1
=(10-9)×(10+9)+(8-7)×(8+7)+(6-5)×(6+5)+(4-3)×(4+3)+(2-1)×(2+1)
=10+9+8+7+6+5+4+3+2+1
=(10+1)×10÷2
=55

6. 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9=

1x2 + 2x3 + 3x4 + .+ n(n+1) = 1/3 * n(n+1)(n+2)
  1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9
  = 1/3 * 8 * 9 * 10
  = 240

7. 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11

1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11
  =10×（10+1）×（10+2）÷3
  =10×11×12÷3
  =110×12÷3
  =1320÷3
  =440

8. 1x2=3 2x3=5 4x6=20 5x8=39 那么 7x11=?

1x2x3/1x3x4=2x4x6/2x6x8=------=nx2nx3n/nx3nx4n=1/2
  [(1x2x3+2x4x6+...+nx2nx3n)/(1x3x4+2x6x8+...+nx3nx4n)）=1/2
  根号[(1x2x3+2x4x6+...+nx2nx3n)/(1x3x4+2x6x8+...+nx3nx4n)）
  =根号(1/2)
  =(根号2)/2