Dear Allan, First of all, thank you for your 50 years of commitment and hard work on your excellent Puzzle Corner. You and I overlapped a little at MIT, but I was going for my PhD in EE.  I entered MIT as a PhD student in 1966. I am writing to you about problem N/D 3.  I had always been interested in the various means, so this problem piqued by interest.  So, I sent it to a couple of colleagues, one of whom is Professor Amro El-Jaroudi at the University of Pittsburgh. Amro discovered two things.  First, there is an error in the published proof.  (In the abbreviated form in TR, p. 63, right column, the equation after "from which determine" is incorrect.)  I sent Amro the full proof on your web site, so he proceeded to write a correct proof (attached). The second thing that Amro discovered has to do with the limit of the iteration for very large b0.  The problem asks: "what is the limit when a0=1 and b0 is large"?  Amro and I both took this to mean that the problem was seeking a formula for that limit when b0 is very large, i.e., as it approached infinity.  So, when I saw the solution to the problem in the recent issue (and the expanded version on your web site), I did not see any such formula.  As it turns out, Amro had already found that formula but did not submit it.  He found that the limit as b0 approached infinity is: L(1, b0) => pi/2 * b0 / ln(b0) For lower values of b0, the above formula appears to be always an overestimate.  Amro would be happy to send you a proof for that formula if you wish. Thanks again and all the best to you. John