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Re: [obm-l] Desigualdade envolvendo a sequencia dos primos

To: obm-l@xxxxxxxxxxxxxx
Subject: Re: [obm-l] Desigualdade envolvendo a sequencia dos primos
From: "saulo nilson" <saulo.nilson@xxxxxxxxx>
Date: Sat, 19 Apr 2008 19:34:20 -0300
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se eu por k=oo o pn sempre vai ser menor do que n^oo, tem que provar que e valido para k=2?

On Mon, Apr 7, 2008 at 10:50 AM, Artur Costa Steiner <artur.steiner@xxxxxxxxxx> wrote:

Acho este problema interessante. Encontrei uma solucao, gostaria de ver como os colegas resolvem.

Seja p_n, n =1,2,3.... a sequencia dos numeros primos. Mostre que, para todo k > 1, a desigualdade,

p_n < n^k

ocorre para uma infinidade de índices n.

Follow-Ups:
- RES: [obm-l] Desigualdade envolvendo a sequencia dos primos
  - From: Artur Costa Steiner

References:
- Re: [obm-l] lim (n --> oo) e^(-n) (1 + n + (n^2)/2!...+(n^n)/n!)
  - From: Carlos Nehab
- [obm-l] Desigualdade envolvendo a sequencia dos primos
  - From: Artur Costa Steiner

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