Recent content by sobolev

The following is a proof of convergence. I think it is a little more transparent than rudinreader's but due credit must be given to rudinreader as his proof provides the backbone for this one. (1) The first thing of note is... \frac{ log( log( n! ) ) }{ log(n) } \rightarrow 1 Which...

Nicely done rudinreader. I calculated my values using Stirling's series (in its convergent form) which was actually your first suggestion.

Anybody else calculate a_4 and a_5 to verify my values?

Nicely done!

Sounds interesting. Also I would like to see how you guys would go about proving convergence of the sequence. The one thing I couldn't do was come up with a closed form expression for the value. The person who set the problem couldn't either so I didn't waste too much time on this.

Okay some more carrot: a_5 = 2.1164259 Anybody solve it on their own?

I don't want to tell you how I solved the problem for a good reason. I found it to be quite interesting and I want to see other creative and unique ideas for solving it. If I tell you how I did it then I probably will not see other creative approaches. Here is some carrot: a_4 = 2.1164259

Of course you will get overflow error if you compute it the naive way. The idea is to write it in a different form so you can calculate it without overflow. I have already solved the problem. Just interested in what others have to say about it.

Even just a discussion on the sort of approaches that people would take to solve such a problem would be interesting.

Can any of you solve this? :smile: Firstly, some notation: Let \Pi(x) = \Gamma(x+1) where \Gamma(x) is the usual gamma function i.e. an extension of the factorial to the complex numbers. Let log^{n} (x) = log( log( \cdots log( x ) ) ) where log is applied n times to x e.g. log^{4} (x) = log(...