Z to the M, over one minus Z to the M plus one. and as we saw special number sequences like the binomial coefficients arise when we're studying algorithms and combinatorial structures. so with generating functions we can work with all these kinds of sequences with just one function. so oh, and this is just dividing by, dividing out z to the n, we get a slightly different look at that same generating function. and we'll have use for applying all of these equations which are in tables in the book later on. okay, we can go the other way and we can integrate. if you have a OGF if you integrate it from zero to Z. if you do it term by term the definition, you see that, that gives us the OGF of the sequence, A1 over two, A2 over three and so forth. so, taking our standard integrating it. 