简算:1/1*3+1/3*5+1/5*7+1/7* - 知识问答

简算:1/1*3+1/3*5+1/5*7+1/7*9+1/9*11

3个回答

1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
=(1/2)(1/1-1/3)+(1/2)(1/3-1/5)+(1/2)(1/5-1/7)+(1/2)(1/7-1/9)+(1/2)(1/9-1/11)
=(1/2)[1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11]
=(1/2)(1-1/11)
=(1/2)(10/11)
=5/11

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