I have this given assignment, and I need a couple of hints to get me started since I don't know how to do this. what is the generating function for the given series: $\{ 1,3,5,7,9 \}$?
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Let $a_n=2n-1$. – R.N Nov 26 '15 at 14:19
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I see your solution is right. But in an answer i cant just write that ( i think). It's more like i need a general solution-method for these kinds of questions. – kirkegaard Nov 26 '15 at 14:25
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Ancient art called observation, and knowledge of number line aka something which looks like the series ${1,2,3,4,...}$ might come handy at times. Rest, and a general solution method is a mystery yet to be solved. – Jesse P Francis Nov 26 '15 at 15:20
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The generating function $g$ for the (finite) sequence $(1,3,5,7,9)$ is the function defined by$$g(s)=1+3s+5s^2+7s^3+9s^4.$$ – Did Nov 26 '15 at 17:07
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There are many sequences whose first five terms are 1, 3, 5, 7 and 9. As an example, consider $$a(n) = 5 - \frac{n}{20} (n - 3) (n - 6) ((n - 3)^2 + 4) \text{ for } n=1, \ldots, 5.$$ For other possibilities, you can check The On-Line Encyclopedia of Integer Sequences, which has 400+ results for this, including the popular a(n) = 2n+1 similar to the one mentioned in the comments.
Helder
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