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Math Help - real-valued sequences

  1. #1
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    real-valued sequences

    . Let
    {xn} and {yn} be real-valued sequences.
    Suppose xn + and {yn} is bounded. Prove that yn / xn 0 .
    how can i use the definitions of xn converges + to and yn is bounded to prove this. and what value of epselon can i choose to show that the absuolt value of xn/yn is less that epselon. I will appraciate your help. Thanks.

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  2. #2
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    Quote Originally Posted by koko2009 View Post
    . Let









    {xn} and {yn} be real-valued sequences.

    Suppose xn + and {yn} is bounded. Prove that yn / xn 0 .
    how can i use the definitions of xn converges + to and yn is bounded to prove this. and what value of epselon can i choose to show that the absuolt value of xn/yn is less that epselon. I will appraciate your help. Thanks.

    Hint: \exists M\,\,s.t.\,\,\forall n\in \mathbb{N}\,,\,|y_n|\leq M\,,\,\,and\,\,\forall \epsilon >0\,\,\,\exists \,N_{\epsilon}\in \mathbb{N} \,\,s.t.\,\,n>N_{\epsilon}\Longrightarrow\,x_n>\fr  ac{M}{\epsilon}

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