Posted: Tue Jul 20, 2004 11:40 pm    Post subject: Number problem

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))=?

Posted: Wed Jul 21, 2004 1:31 pm    Post subject: Re: number problem

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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