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Unbounded sequence

  1. Oct 19, 2008 #1
    1. The problem statement, all variables and given/known data

    show that the following sequence is unbounded

    {xn}= [(n+1)/n]^3 - n^3

    2. Relevant equations



    3. The attempt at a solution

    I expanded it but didnt get anywhere after that. I know that a sequence is unbounded if for all M>0 there exists N such that abs(xN)>M but i still dont understand how to show it.
     
  2. jcsd
  3. Oct 19, 2008 #2

    Tom Mattson

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    Here's something to try: Consider the following function of a real variable.

    f(x)=[(x+1)/x]^3-x^3

    Now take the derivative and show that f is monotonically decreasing for all x>0, and that the range of f is (0,infinity) when x>0. (sorry, LaTeX is acting funny)

    What then can you conclude about f(n)?
     
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