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 Mar20 revised Suplement books for calculus course? added 131 characters in body Mar16 comment Help on Apostol's explanation of Archimedes method? @neuguy For example, why start with $(k+1)^3$? I'm not really sure of what is happening in there, then I asked it vaguely: I was hoping that someone could rephrase it adding a little bit more detail perhaps? Mar16 asked Help on Apostol's explanation of Archimedes method? Mar16 revised Suplement books for calculus course? added 74 characters in body Mar15 asked Suplement books for calculus course? Feb27 awarded Yearling Feb23 comment How to solve this distribution problem with generating functions? @Taussig Sorry,I meant 3 boxes. I forgot to add it. Feb23 revised How to solve this distribution problem with generating functions? added 4 characters in body Feb23 asked How to solve this distribution problem with generating functions? Feb19 comment Is it possible to represent any sequence as the coefficients of arbitrary generating functions? @whacka What's the meaning of sufficiently radical? I googled it and most of the results are about radical christianism(?!) and suffixing "math", yields something that also seems completely unrelated. Feb18 comment Is it possible to represent any sequence as the coefficients of arbitrary generating functions? @whacka Got it. I got curious on a generating function which can't be expressed in a nice closed-form. Could you give me an example? Feb18 comment Is it possible to represent any sequence as the coefficients of arbitrary generating functions? @whacka The problem is here: "you can form a corresponding generating function". I've looked (in my lectures) at few methods for finding generating functions. They are basically the expansion $(1-x)^n$ and $\left[ \frac{1}{1-x} \right]^n$, derivating and integrating one series and performing the sum/multiplication of two series. With this, it's not really clear that every sequence could be produced in the coefficients of the generating function. Feb17 comment On the calculus of recurrence relations using generating functions? Oh, I got it. I was being stupid of not checking it by expanding a few terms. I did it now and I noticed they are the same. $$a_0+\sum_{k\ge 1}(ba_{k-1}x^k+cx^k)=a_0+(ba_0x^1+cx^1+\cdots)+(ba_1x^2+cx^2+\dots)$$ $$a_0+bx\sum_{k\ge 0}a_kx^k+cx\sum_{k\ge 0}x^k=a_0+(ba_0x^1+ba_1x^2+\dots)+(cx^1+cx^2+ \dots )$$ Feb17 comment On the calculus of recurrence relations using generating functions? I guess this part is not clear: $$a_0+\sum_{k\ge 1}(ba_{k-1}x^k+cx^k)=a_0+bx\sum_{k\ge 0}a_kx^k+cx\sum_{k\ge 0}x^k$$ Do we push the $bx,cx$ outside the summation because they have already been processed by $\sum_{k\geq 1}$? I guess this make sense because the next summations start from $k\geq 0$. Feb17 asked On the calculus of recurrence relations using generating functions? Feb17 comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears? Is it a general idea that I can leave the higher powers to simplify it? Aren't there ocasions when such procedure fails? Feb17 comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears? Why only the coefficient of $x^{11}$? Don't you need to count the coefficients of $x^{11},x^{10},x^{9}$? There is (for example) the ocasion when each kid has $3$ oranges, no? Feb17 comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears? @N.F.Taussig Yes. Feb16 comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears? @Uncountable Yes, it was a typo. Thanks. Feb16 asked In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears?