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Math Help - show limit approaches 0

  1. #1
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    show limit approaches 0

    whats the proper way of showing that 1/(4n^2 + 1) goes to 0? when you have a n on both the top and the bottom you could just divide top and bottom by n. but could you do the same for this problem even though there isnt a n on the top to get (1/n^2) / (4 + 1/n^2) = 0/4 = 0?
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  2. #2
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    Quote Originally Posted by jeph View Post
    whats the proper way of showing that 1/(4n^2 + 1) goes to 0? when you have a n on both the top and the bottom you could just divide top and bottom by n. but could you do the same for this problem even though there isnt a n on the top to get (1/n^2) / (4 + 1/n^2) = 0/4 = 0?
    Use the following theorem.

    Theorem: Let {s_n} be a sequence of non-zero terms. Then, lim s_n = 0 if and only if lim 1/s_n = +oo.
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