# Sequences

• Oct 10th 2008, 09:31 AM
Showcase_22
Sequences
I have another post about sequences but this question seems easier (hence why I posted it here!).

However, "easier" is used relative to the other question I am stuck on (posted in Advanced Algebra).

The problem is:

Quote:

Think of an example to show that the statement,

if $(a_n) \rightarrow 0$ then $\frac{1}{a_n} \rightarrow \infty$

is false, even if $a_n \neq 0$ for all n
All the equations I have tried have failed. I can't think of a method to do this question properly =(

Any ideas would be greatly appreciated!
• Oct 10th 2008, 09:49 AM
Plato
$\left[ {\frac{{\left( { - 1} \right)^n }}
{n}} \right] \to 0$

But what about $\frac{1}
{{\left| {a_n } \right|}}$
?
• Oct 10th 2008, 11:32 AM
nmatthies1
Exactly.

Think of a non-monotonic sequence that tends to zero, ie. that approaches zero from the "-ve and the +ve side".

(-1)^n/n is a good example.
• Oct 10th 2008, 12:26 PM
Showcase_22
I thought of it that way but couldn't quite grasp the concept.

I was trying sequences like $a_n=\frac{sin n}{n}$. Unfortunately this equals zero so it didn't work!

thanks for the help guys!
• Oct 10th 2008, 12:34 PM
Showcase_22
lol, I didn''t see it!

boy is my face red!

So have you done the section about $\pi$ yet? It's really confusing!