求1/1*5+1/5*9+1/9*13+1/13* - 知识问答

求1/1*5+1/5*9+1/9*13+1/13*17+…+1/2001+2005的过程与答案

5个回答

1/1*5=(1/4)(1/1-1/5)
1/5*9=(1/4)(1/5-1/9)
...
1/2001*2005=(1/4)(1/2001-1/2005)
1/1*5+1/5*9+1/9*13+1/13*17+…+1/2001*2005
=(1/4)(1/1-1/5+1/5-1/9+..+1/2001-1/2005)
=(1/4)*(1-1/2005)
=(1/4)*2004/2005
=501/2005

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