1/1*2+1/2*3+1/3*4+.+1/2004*2005+1/2005*2006

1/1*2+1/2*3+1/3*4+.+1/2004*2005+1/2005*2006
1/1*2+1/2*3+1/3*4+.+1/2004*2005+1/2005*2006

1/1*2+1/2*3+1/3*4+.+1/2004*2005+1/2005*2006
1/1*2+1/2*3+1/3*4+...1/2004*2005+1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+.+1/2004-1/2005+1/2005-1/2006
=1-1/2006
=2005/2006

解
原式
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2005-1/2006)
=1+(1/2-1/2)+(1/3-1/3)+……+(1/2005-1/2005)-1/2006
=1-1/2006
=2005/2006看不懂怎么办？看书我有更简单的方法了，不过我不想谢你耶······有更简单的方法，那我应该请教你了抵消喽这不是废话，...

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解
原式
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2005-1/2006)
=1+(1/2-1/2)+(1/3-1/3)+……+(1/2005-1/2005)-1/2006
=1-1/2006
=2005/2006

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