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Μη μαν ασπουδι γε και ακλειως απολοιμην

Archive for June, 2007

BJJ blogs I read

Posted by nugae on 27 June 2007

There are more and more blogs on Brazilian jiu-jitsu. I try not to read too many of them, because for me BJJ is something you learn with the body, not with the head.

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Posted in BJJ | 5 Comments »

A mathematical problem

Posted by nugae on 11 June 2007

This problem is in two parts. Part A is A-level standard; part B is more advanced.

A. Given that k > 1.0, prove that, for large n, the largest real root of

(x+1)^{n}=kx^{n}

approaches

x\sim\frac{n}{\ln k}-\frac{1}{2}

B. Given that k > 1.0, prove that, for large n, the largest real root of

B_{n+1}(x+1)=kB_{n+1}(x)

approaches

x\sim\frac{n}{\ln k}+\frac{1}{k-1}+\frac{1}{2}

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Posted in Cyprian's Last Theorem, mathematics | Leave a Comment »