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
approaches
B. Given that k > 1.0, prove that, for large n, the largest real root of
approaches
Equation B is equivalent to
The Bernoulli polynomials 
are described in MathWorld and Wikipedia. Numbering schemes differ: this problem uses what MathWorld describes as the “new” definition, with the first few polynomials being:
This entry was posted on 11 June 2007 at 17:57 and is filed under Cyprian's Last Theorem, mathematics.
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