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Math Help - 2 limit of product problems

  1. #1
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    2 limit of product problems

    \lim_{x \mapsto \infty }(\frac{1}{n}\prod_{k=2}^{n}\frac{k^{3}-1}{k^{3}+1}sin\frac{n^{2}}{\pi })

    \lim_{x \mapsto \infty }(\prod_{k=2}^{n}\frac{(k-1)(k+1)}{k(k+2)}cos\frac{n! + 100}{n^{2}} )


    anyone knows how to solve these two ?
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  2. #2
    Super Member girdav's Avatar
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    Re: 2 limit of product problems

    For the first, the product is \leq 1 and for the second, it's telescopic.
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  3. #3
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    Re: 2 limit of product problems

    x -> infinity but neither expression has x... is it n that should approach infinity?
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  4. #4
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    Re: 2 limit of product problems

    yeah, its n, sorry about that, its a mistake.
    @girdav maybe procedure?
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  5. #5
    Super Member girdav's Avatar
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    Re: 2 limit of product problems

    Where are you stuck?
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  6. #6
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    Re: 2 limit of product problems

    well, I know that i must develop product, so when i do it, then cancel whats possible in nominator and denominator, and lets say i had left some for etc (n+1)/(n+2), what shoud i do with cos (n!+100)/n^2 ?, or in the 1st problem, when i develop product, and cancel whats possible, what to do with sin(...) ?
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