Question

一道小学数学题:1/6+1/12+1/20+1/30+..........+1/2005*2006=?(要算式)

Answer 1

1/6+1/12+1/20+1/30+..........+1/2005*2006=
1/2*3+1/3*4+1/4*5......+1/2005*2006=
1/2-1/3+1/3-1/4+1/4...........-1/2005+1/2005-1/2006=
1/2-1/2006=1002/2006=501/1003

Answer 2

原式=(1/2-1/3)+(1/3-1/4)+.....+(1/2004-1/2005)+(1/2005-1/2006)
=1/2-1/2006
=501/1003

Answer 3

原式=1/2-1/3+1/3-1/4+1/4-1/5^......+1/2005-1/2006
= 1/2-1/2006=501/1003

Answer 4

1/6=1/2*3=1/2-1/3,以此类推，全销了，只剩下首项和尾项。自己动手作啊。