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I Can't Find much information on this subject that I can easily understand (I'm not the best at maths).. I'm taking a combinatorics class and our teacher got to generating functions. He stated that we can model dice roll with the function

$$f(x)= x + x^2 + x^3 + x^4 + x^5 + x^6$$

My question is why can we do this? What does "x" mean in this function and was does $x + x^2 + x^3 + x^4 + x^5 + x^6$ have anything to do with modeling the rolls of a dice?

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    Perhaps he meant that $f(x)=a_1x+\cdots+a_nx^n=\sum _{n=0}^{\infty}a_nx^n$ where $a_n$ is the number of ways to get $n$ by rolling one dice. – 2017-02-14
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    The $x$ doesn’t really mean anything. It’s just a placeholder. The important thing is the coefficients of the powers of $x$. Basically, you’re packaging up a sequence of numbers into a single object—the power series on the right. What makes this technique interesting is that for many common sequences, these power series have relatively simple closed-form expressions that let you manipulate them more easily. – 2017-02-14
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    The idea is that the coefficient of $x^{s}$ in $f(x)^{d}$ is the number of ways you can get the sum $s$ when rolling $d$ dice. – 2017-02-14

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