Proving Unboundedness of {xn} with [(n+1)/n]^3 - n^3

[sara_87]

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 don't understand how to show it.

 

[quantumdude]

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)?