# Thread: Obtaining a sequence in a set converging to supS and infS

1. ## Obtaining a sequence in a set converging to supS and infS

2. I've figured out A.. I just need help with B.

3. Originally Posted by qtpipi

if my intuition is correct without any solid proof the sequences in concern are:

$\displaystyle \frac{2+(-1)^n}{n}$ and $\displaystyle \frac{2+(-1)^n}{n}+1$

or the sequences $\displaystyle \frac{3}{2k}+1$ and $\displaystyle \frac{1}{2k+1}$ which are the two subsequences of the major sequence

4. $\displaystyle S = \left\{ {\frac{{2 + \left( { - 1} \right)^n }} {n}:n \in \mathbb{Z}^ + } \right\},~\inf (S) = 0,~\sup (S) = \frac{3}{2}$.
Clearly there are subsequences converging to 0 but none converging to $\displaystyle \frac{3}{2}$.

5. But for n=2 $\displaystyle s_{2}=\frac{2+1}{2} = \frac{3}{2}\geq 1$???

And $\displaystyle s_{2}\in S$ ???

6. Originally Posted by xalk
But for n=2 $\displaystyle s_{2}=\frac{2+1}{2} = \frac{3}{2}\geq 1$???
You are quite right. I corrected the mistake.