La p-serie



  1. Convergencia y divergencia de P-Series
    Determina si las siguientes series son convergentes o divergentes:
    1. n=31n2 \large \sum_{n=3}^{\infty}\frac{1}{n^2}
    2. n=1n3+1n2 \large \sum_{n=1}^{\infty}\frac{n^3\,+\,1}{n^2}

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Topic Basics
En esta lección hablaremos sobre la p-serie.
La serie de las p, o p-serie se ve muy similar a una serie armónica pero en este caso la serie puede ser convergente o divergente. Su convergencia o divergencia depende del exponente en el denominador, llamado “p”.

n=11np \large \sum_{n=1}^{\infty}\frac{1}{n^p}

  • Si p es mayor a 1, entonces la serie es convergente.
  • Si p es menor que 1, entonces la serie es divergente.
  • Si p es igual a 1, entonces la serie es armónica.