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Math Help - converge

  1. #1
    Senior Member sfspitfire23's Avatar
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    converge

    If a_n converges to 0, does \frac{a_n}{2} converge to 0?
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    yes.
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  3. #3
    Senior Member sfspitfire23's Avatar
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    thx
    Last edited by sfspitfire23; April 24th 2010 at 01:03 PM.
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by sfspitfire23 View Post
    is there a theorem that tells me if the series of a_k is convergent then the series of a_k/2 is convergent?
    The quotient property of convergent sequences: If a sequence a_n converges to a number a, and the sequence b_n converges to a number b, with b_n not equal to 0 for all indices n, and b is not equal to 0, then the sequence of quotients \frac{a_n}{b_n} converges to the quotient \frac{a}{b}.

    lim (n\rightarrow \infty) [\frac{a_n}{b_n}] = lim (n\rightarrow \infty) [a_n \times \frac{1}{b_n}]= a \times \frac{1}{b} = \frac{a}{b}
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