series

[sofia]

I'm having some trouble...what's the formula for the series {5,1,5,1,5,1...}?

 

[pka]

It can be as easy as \(\displaystyle \L
s_n = \left\{ \begin{array}{l}
5,\quad \mbox{if n is odd}\\
1,\quad \mbox{if n is even} \\
\end{array} \right.\)

Or it can be as complicated as \(\displaystyle \L
s_n = \bmod \left[ {\left( {6n + \left( { - 1} \right)^n } \right),6} \right]\)

 

[robbwrr]

\(\displaystyle \text{Or simply: } s_n = 3 - 2(-1)^n\)

 

[daon]

\(\displaystyle \L\\
5 - 2[1+(-1)^{n-1}]\)

Assuming n starts at 1...