Solving Delta Epsilon Proof (Given Epsilon)

Quote:

Originally Posted by penguinpwn

I read over the guide stickied at the top of the forum, but I did not understand the section on solving proofs when given a particular epsilon value. Could someone walk me through it with the attached problem?

perhaps it's better to show you what is that $\epsilon$ region ...

you will (if not yet) have sequence which $a_n = (-1)^n$ (which don't converge) . why is that. well if you assume different , that for some $a \in \mathbb{R}$ there is $\lim_{n \to \infty } x_n = a$ now you realize that all members of that sequence are going to either one or negative one, that means that in any $\epsilon$ region around point "a" there should be both members of that sequence. that can't be true because if you chose any $\epsilon < \frac {1}{2}$ there is no chance that both that numbers be in some region $(a-\epsilon , a+ \epsilon)$ which length is less than one :D