Question

孩子不会做的题，帮忙解解

从计算结果中找出规律，利用规律性计算1/1*2+1/2*3+1/3*4+1/4*5+---------+1/2009*2010=？
不好意思打错了，补充一下
1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,1/4*5=1/4-1/5,.........
从计算结果中找出规律，利用规律性计算1/1*2+1/2*3+1/3*4+1/4*5+---------+1/2009*2010=？

Answer 1

1×1/2+1/2×1/3+1/3×1/4+.....+1/2009×1/2010
=（1 - 1/2）+(1/2 - 1/3 )+(1/3 - 1/4 )+......+(1/2009 - 1/2010 )
=1 - 1/2+1/2 - 1/3 +1/3 - 1/4 +......+1/2009 - 1/2010
=1 - 1/2010
=2009/2010

Answer 2

1/1*2+1/2*3+1/3*4+1/4*5+---------+1/2009*2010 =1×1/2+1/2×1/3+1/3×1/4+.....+1/2009×1/2010
=（1 - 1/2）+(1/2 - 1/3 )+(1/3 - 1/4 )+......+(1/2009 - 1/2010 )
=1 - 1/2+1/2 - 1/3 +1/3 - 1/4 +......+1/2009 - 1/2010
=1 - 1/2010
=2009/2010

Answer 3

1×1/2+1/2×1/3+1/3×1/4+等+1/2009×1/2010
=（1 - 1/2）+(1/2 - 1/3 )+(1/3 - 1/4 )+等+(1/2009 - 1/2010 )
=1 - 1/2+1/2 - 1/3 +1/3 - 1/4 +等+1/2009 - 1/2010
=1 - 1/2010
=2009/2010

Answer 4

1/1*2+1/2*3+1/3*4+1/4*5+---------+1/2009*2010=1－1/2+1/2－1/3+1/3－1/4+1/4－1/5+---------+1/2009－1/2010=1－1/2010=2009／2010　

Answer 5

(1－1/2)+(1/2-1/3)+(1/3-1/4)+---------(1/2009-1/2010)
=1-1/2010
=2009/2010

Answer 6

相加，中间的都能消掉，仅剩1/2-1/2010