# Thread: generating functions

1. ## generating functions

determine the sequence generated by (6-2x)/(1+2x-15x^2)

2. Originally Posted by stumped765 determine the sequence generated by (6-2x)/(1+2x-15x^2)
What have you tried? Have you tried decomposing this rational function? Once you have this becomes an elementary application of the geometric series.

3. yah i got (6-2x)/(5x+1) *(6x-2)/(3x-1)
but I guess im confused about what the numerator tells me about the sequence like i know what to do if it was jsut 1/(5x+1) or 1/(3x-1) but the numerator throws me for a loop.

4. Originally Posted by stumped765 yah i got (6-2x)/(5x+1) *(6x-2)/(3x-1)
but I guess im confused about what the numerator tells me about the sequence like i know what to do if it was jsut 1/(5x+1) or 1/(3x-1) but the numerator throws me for a loop.
Use partial fractions decomposition. It should give you that

$\displaystyle \frac{6-3x}{-(3x-1)(5x+1)}=\frac{33}{8(5x+1)}-\frac{15}{8(3x-1)}$

Now use that $\displaystyle \frac{1}{1-z}=\sum_{n=0}^{\infty}z^n$

IF this is indeed what you are looking for the first term should give that $\displaystyle \sigma_n=\frac{33}{8}(-1)^n5^n$. Now find $\displaystyle \delta_n$ for the second one. And your function will be the generator of $\displaystyle \sigma_n+\delta_n$

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