A new approach on the urn problem : semi-convergent series.
- From: Denis Feldmann <denis.feldmann.asupprimer@xxxxxxxxxxxxxxxx>
- Date: Sat, 06 Jan 2007 17:48:32 +0100
If U_n(a)= 1/(10n-9)^a + 1/(10n-8)^a + 1/(10n-7)^a+...+ 1/(10n-1)^a +1/(10n)^a -1/n^a, U_n(a) simulates the operation at time n of putting ten balls in the urn marked 10n-9,...,10n and of removing ball n, and the sum of series S(a)=sum(U_n(a), n=1..infinity) should give a good idea of what is in the urn "at the end". But in fact, S(a)=0 if a>1, S(1)= ln(10) (a nice exercise, that one) and S(a) diverges (towards +oo) if a<1...
.
- Prev by Date: Re: Set Theory question
- Next by Date: Re: convergence of series sum_{n=1}^{\infty} ( 1-1/sqrt(n) )^n
- Previous by thread: Re: Belt trick for spin 3/2
- Next by thread: Real roots?
- Index(es):
