(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex]x_m = 1 + \frac{1}{2} + \frac{1}{3} + ... \frac{1}{m}, m \in N[/tex].

Prove [tex]x_m[/tex] is not bounded above and therefore [tex]x_m[/tex] does not converge.

2. Relevant equations

We know from our class an important theorem stating that:

If sequence converges then the sequence is bounded.

Thus we can say if the sequence is not bounded then it is not convergent.

3. The attempt at a solution

By above (#2), i just have to show our sequence is not bounded. This means i have the following claim:

[tex]x_m[/tex] is not bounded above if and only if given any S > 0 , there exists m such that [tex]x_m[/tex] > S.

Question:

1. Do i have to prove both sides of the arguement (if and only if)? Or can I just change my claim to a one sided (left to right)?

2. Can someone help me formulate some thoughts on how to begin this proof?

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# Homework Help: Bounded sequence

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