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Benko
Frequent VisitorJoined: 16 Jul 2004Posts: 33
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Posted: Tue Jul 20, 2004 11:40 pm Post subject: Number problem
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1.Prove that for n>1, 1+1/2+1/3+1/4+…+1/n is not an integer.
2.(1-1/(2^2))(1-1/(3^2))…(1-1/(n^2))=?
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Peter
Frequent VisitorJoined: 18 Jan 2004Posts: 128
Location: Hong Kong
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Posted: Wed Jul 21, 2004 1:31 pm Post subject: Re: number problem
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1. For any integer , there exists an integer k such that .
Write , where is an integer.
Now is divisible by but not .
And for all integer , , i is not divisible by . Therefore is even.
However, is odd since is divisible by . Therefore is also odd.
Hence , which is not an integer.
2. Simply make use of .
_________________
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