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Thread: Equivalent

  1. Jul 13th 2010, 12:56 PM #1
    joaopa
    joaopa is offline
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    Equivalent

    Hi everybody,

    Any idea to solve this problem: One denotes \mathbb N=\{0,1,\cdots\}.

    Let (L_n)_{n\in\mathbb N} be a positive non-decreasing sequence such that L_n\underset{n\to+\infty}{\sim}q^n with q>0.

    Then, for every n\in\mathbb{N}
    \sum_{\substack{u_1+\cdots+u_{n+1}=j-n\\u_1\ge0,\cdots,u_{n+1}\ge0}}\limits L_{u_1}L_{u_2}\cdots L_{u_{n+1}}\underset{j\to+\infty}{\sim}L_j\binom{j }{n}.

    Thanks in advance
    Last edited by joaopa; Jul 13th 2010 at 10:47 PM.
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