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Math Help - Prove Sequence is Convergent

  1. #1
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    Prove Sequence is Convergent

    Use the definition of convergence to prove the sequence is convergent.
    {(5n+17)/(2n)}

    We have to prove the sequence converges to 5/2.
    e>0, the n>= N
    |[(5n+17)/(2n)] - [5/2]| = |17/(2(2n))|
    There is where I am get stuck. I know we have to choose a postive integer N it is <e. Where do I go from here?
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  2. #2
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    Quote Originally Posted by summerset353 View Post
    Use the definition of convergence to prove the sequence is convergent.
    {(5n+17)/(2n)}
    Here is a mistake. \left| {\frac{{5n + 17}}{{2n}} - \frac{5}{2}} \right| = \frac{{17}}{{2n}}.

    So find a N such that \frac{{17}}{{2N}} < \varepsilon .
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