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Unbounded sequence

  • Thread starter sara_87
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  • #1
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Homework Statement



show that the following sequence is unbounded

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

Homework Equations





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.
 

Answers and Replies

  • #2
Tom Mattson
Staff Emeritus
Science Advisor
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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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