Sequences
- Thread starter rinspd
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pka
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- Jan 29, 2005
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Because there are literally numerous ways of doing this, I will give you one:
\(\displaystyle a_n=4\left( {n - 2\left\lfloor {\frac{n}{2}} \right\rfloor } \right) + 1\).
One can generate the sequence {0,1,0,1,...} with:
\(\displaystyle \frac{[1+(-1)^n]}{2}\)
You can easily turn this into a sequence for {a,b,a,b...} with one simple modification.
Another way: 0.151515... is a rational number: 15/99. Notice that multiplying by 10 moves a 1 to the units digit. Then again, it will become a 5.
\(\displaystyle a_n = \lfloor 10^n\cdot 15/99 \rfloor \,\, \text{(mod 10)}\)
\(\displaystyle \frac{[1+(-1)^n]}{2}\)
You can easily turn this into a sequence for {a,b,a,b...} with one simple modification.
Another way: 0.151515... is a rational number: 15/99. Notice that multiplying by 10 moves a 1 to the units digit. Then again, it will become a 5.
\(\displaystyle a_n = \lfloor 10^n\cdot 15/99 \rfloor \,\, \text{(mod 10)}\)