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Math Help - Limit for series

  1. #1
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    Limit for series

    \lim_{x\to\infty}\frac{n!}{2n! + 1} = \frac{1}{2}

    How is this so exactly? Is \infty plugged in? And I don't see algebraically how to cancel n!
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  2. #2
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    Quote Originally Posted by Retromingent View Post
    \lim_{x\to\infty}\frac{n!}{2n! + 1} = \frac{1}{2}

    How is this so exactly? Is \infty plugged in? And I don't see algebraically how to cancel n!
    Factor out n! from the numerator and the denominator

    =\frac{n!}{n!} \times \frac{1}{2+\frac{1}{n!}}=\frac{1}{2+\frac{1}{n!}}
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  3. #3
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    I was going to say that since n! will obviously be much larger than the constant, you only need to look at the coefficients of n!. The same holds true for powers, you only need to look at the highest power, since \lim_{n \rightarrow \infty} n^3 rises much faster than \lim_{n \rightarrow \infty} n^2
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