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Convergent?

Convergent?  
Eamon Warnock
From:Eamon Warnock
Subject:Convergent?
Date:Sun, 23 Jan 2005 18:45:31 +0000 (UTC)
Prove the convergence or otherwise of

1/1 + 1/2(1+log2) + 1/3(1+log3)(1+log(1+log3)) +
1/4(1+log4)(1+log(1+log4))(1+log(1+log(1+log4))) + ...


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