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okay im supposed to find a recurrence relation for

$$ a_{n+1}= b \cdot a_n + c \cdot n \ \ \ \ \ \ \ \ \ \ \ \ \mathbf{(1)} $$

where $b$ and $c$ are constants. the method we learned in class was to multiply each term by $x^n$ and then take the sum of of the equation which has always worked fine but the "$c \cdot n$" term is giving me trouble in this problem. after some manipulation i get $c \sum n \cdot x^n$ which obviously does not converge. i know $x^n$ converges to $1 \over{1-x}$ but i dont know what to do about the "$n$" term. any help would be appreciated.

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    For the last bit, see http://math.stackexchange.com/questions/38194/finding-the-sum-of-a-series. It's a FAQ...2012-04-03
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    Consider reading [this](http://math.stackexchange.com/editing-help), and especially [this](http://math.stackexchange.com/editing-help#latex) section.2012-04-03
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    You say you are supposed to find a recurrence relation for (1), but that can't be what you mean - (1) is already a recurrence relation. Maybe you mean you are supposed to find a *generating function* for the sequence $a_n$. Or maybe you mean you are supposed to find a *solution* of the recurrence relation (1). I'm not just quibbling here - half the trouble students have with math is getting all muddled up because they don't use the vocabulary precisely. Figure out what question you really mean to ask, and then edit the question accordingly - it's worth it.2012-04-03
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    @GerryMyerson You make a completely valid and important point; though, I don't think the consequences are all that serious with the misuse of terminology in this post. And, +1 for providing the correct phraseology.2012-04-03

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