limit superior ....

Aug 2008
172
1
Find \(\displaystyle \overline{lim} \ a_n \) where :
\(\displaystyle a_n = \begin{cases}
1 &, \text{ if } n\ is \ square \\
0 &, \text{ if } n \ not \ square
\end{cases} \)
 

Drexel28

MHF Hall of Honor
Nov 2009
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Berkeley, California
Find \(\displaystyle \overline{lim} \ a_n \) where :
\(\displaystyle a_n = \begin{cases}
1 &, \text{ if } n\ is \ square \\
0 &, \text{ if } n \ not \ square
\end{cases} \)
Let \(\displaystyle S\) represent the set of all subsequential limits of \(\displaystyle a_n\). Evidently \(\displaystyle S=\{0,1\}\) and so \(\displaystyle \limsup\text{ }a_n=\sup\text{ }S=1\)