# Limit points

• Oct 27th 2009, 06:32 AM
zeh
Limit points
Sequence: $\frac{1}{2},\frac{1}{4},\frac{1}{2},\frac{3}{4},\f rac{1}{8},\frac{1}{4},\frac{3}{8},\frac{1}{2},\fra c{5}{8},\frac{3}{4},\frac{7}{8},.......$
Find all limit points
• Oct 28th 2009, 05:37 PM
redsoxfan325
Quote:

Originally Posted by zeh
Sequence: $\frac{1}{2},\frac{1}{4},\frac{1}{2},\frac{3}{4},{\ color{blue}\frac{1}{8},\frac{1}{4},\frac{3}{8},\fr ac{1}{2},\frac{5}{8},\frac{3}{4},\frac{7}{8}},.... ...$
Find all limit points

We can't really find out the limit points if we don't know how to define the sequence. The blue sequence above diverges; it's just an arithmetic sequence: $a_n=a_{n-1}+\frac{1}{8}$.

I think we would need more information before we could say definitively what this sequence is doing.