Question

\[a_{n}\] is a sequence \[\in \mathbb{R} \]. if \[|a_{n}|\rightarrow|a| (n \rightarrow \infty)\], then \[a_{n} \rightarrow a (n \rightarrow \infty) \] too , give a short reason why or give an example why its not.

Answer 1

prove?

Answer 2

i added some extra information pls renew your page

Answer 3

Well, simply put, it's false :)

Answer 4

Try \[\Large a _n = (-1)^n\]
^_^

Answer 5

Absolute value is always 1, so the limit is 1 as n goes to infinity, however, without the absolute value, then, the sequence doesn't converge to anywhere, it just alternates :P

Answer 6

:) ok thx