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Math Help - upper bound for a product

  1. #1
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    upper bound for a product

    Hi all,
    anyone knows how to obtain an appropriate upper bound for the following product:

    \prod_{i=1}^{a}(a-i+1)^{(a-i+1)}

    Many thanks in advance!
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  2. #2
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    Quote Originally Posted by oscaralive View Post
    Hi all,
    anyone knows how to obtain an appropriate upper bound for the following product:

    \prod_{i=1}^{a}(a-i+1)^{(a-i+1)}

    Many thanks in advance!
    For example (assuming the notation is standard and a\in\mathbb{N}:

    \displaystyle{\prod\limits_{i=1}^{a}(a-i+1)^{(a-i+1)}=a^a\cdot (a-1)^{a-1}\cdot\ldots\cdot 2^2\cdot 1\leq a^{\frac{a(a+1)}{2}}}
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