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Math Help - find the limit.

  1. #1
    Senior Member
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    find the limit.

    finding the limit of this sequence:

    lim
    n->infinity (cosn)/(sqrt(n))

    While graphing, it looks like the limit is approaching 0.

    however, how could i demonstrate this mathematically?

    could I use l'hopitals rule?

    thankyou.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rcmango View Post
    finding the limit of this sequence:

    lim
    n->infinity (cosn)/(sqrt(n))

    While graphing, it looks like the limit is approaching 0.

    however, how could i demonstrate this mathematically?

    could I use l'hopitals rule?

    thankyou.
    First you need to know that as n \to \infty, \sqrt{n} \to \infty

    0 \le |\cos(n)/\sqrt{n}| \le 1/\sqrt{n}

    hence as n becomes large |\cos(n)/\sqrt{n}| is trapped between zero and a number which becomes arbitarily small, and hence tends to zero. But if the absolute value of a sequence tends to zero so does the sequence itself.
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