# Thread: Intro to Real Analysis.

1. ## 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!

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

3. 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.