# Intro to Real Analysis.

• Nov 13th 2008, 07:39 AM
ilikedmath
Intro to Real Analysis.
The problem asks for us to: Construct a sequence { $s_n$} for which the subsequential limits are {- $\infty$, -2, 1}.

I found some help already:
...the sequence {-n} has the subsequential limit of {- $\infty$},
...the sequence is {-2 - 1/n} has the subsequential limit of {-2}, and
... the sequence {1 - 1/n} has the subsequential limit of {1}.

How do I combine the three sequences to make the one sequence I need for the problem.

Any help, suggestions, corrections, and tips of any kind are greatly appreciated.
Thank you for your time!(Nod)
• Nov 13th 2008, 07:51 AM
red_dog
$\displaystyle s_n=\left\{\begin{array}{lll}-n & ,n=3p\\-2-\frac{1}{n} & ,n=3p+1\\1-\frac{1}{n} & ,n=3p+2\end{array}\right.$
• Nov 13th 2008, 12:45 PM
ilikedmath
Quote:

Originally Posted by red_dog
$\displaystyle s_n=\left\{\begin{array}{lll}-n & ,n=3p\\-2-\frac{1}{n} & ,n=3p+1\\1-\frac{1}{n} & ,n=3p+2\end{array}\right.$

Awesome, our professor did give a hint to go 'piecewise' with this problem.
My only question is, where'd the '3p' come from? I understand that 3p, 3p + 1, and 3p + 2 are three consecutive terms.