- 小学数学竞赛题1\1*2+2\1*2*3+3\1*2*3*4+4
- 1\1*2+2\1*2*3+3\1*2*3*4+4\1*2*3*4*5+5\1*2*3*4*5*6+6\1*2*3*4*5*6*7=(请说明过程)
- 1\1*2+2\1*2*3+3\1*2*3*4+4\1*2*3*4*5+5\1*2*3*4*5*6+6\1*2*3*4*5*6*7
= 1\1*2 + (3-1)\1*2*3 + (4-1)\1*2*3*4 + (5-1)\1*2*3*4*5 +
(6-1)\1*2*3*4*5*6 + (7-1)\1*2*3*4*5*6*7
= [(1/1)-(1/1*2)]+[(1/1*2)-(1/1*2*3)]+ [(1/1*2*3)-(1/1*2*3*4)]+ ...
+[(1/1*2*3*4*5*6)-(1/1*2*3*4*5*6*7)]
= 1 - 1/1*2*3*4*5*6*7
= 5039/5040