Hey there, one of our h/work questions is to prove that a certain sequence is divergent, where xn=(-1)^n for every natural n. I started off by assuming that it was infact convergent so wrote that mod(xn/l)<e where e is any real number greater than zero, and this holds for any n>no. But from the one example we did in class, it seems you can choose your e to make things a little easier for yourself and then choose k and k+1 both greater than no to allow you to obtain the contradiction that you need. I mean I started to try things like mod(xn/l)<1 and then choose mod(xk-l)<1 and (xk+2-1)<1. Then I had 2=mod((k+2)-k) which was equal to mod(xk+2 +xk) but this clearly doesn't seem to get me anywhere (well not from where I'm sitting). I've been trying stuff like this but can't seem to get anything to work. Could someone please put me in the right direction? Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

Btw, when I've written stuff like xk+2 I just mean xsubscript k+2

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# Proving the Divergence of a Sequence

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