1/(1×3)+1/(3×5)+···+1/(2005×2007) 把过程写出来 再写出理由来

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1/(1×3)+1/(3×5)+···+1/(2005×2007) 把过程写出来 再写出理由来
1/(1×3)+1/(3×5)+···+1/(2005×2007) 把过程写出来 再写出理由来

1/(1×3)+1/(3×5)+···+1/(2005×2007) 把过程写出来 再写出理由来
1/1×3+1/3×5+1/5×7+······+1/2005×2007
=1/2[(1-1/3)+(1/3-1/5)+…+(1/2005-1/2007)]
=1/2*(1-1/2007)
=1003/2007

=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)……+[1/n-1/(n+1)]=1/1-1/2+1/2-1/3+1/3-1/4……+1/n - 1/(n+1)=1-1/(n+1)...

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=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)……+[1/n-1/(n+1)]=1/1-1/2+1/2-1/3+1/3-1/4……+1/n - 1/(n+1)=1-1/(n+1)

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