Recent questions tagged generating-functions

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What is the closed form for the generating function for the sequence : 0,1,-2,4,-8,16,-32,64,...
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Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee a...
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Find the following sum.$$\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$$$\frac{20}{41}$$\frac{10}{41}$$\frac{10}{21}$$\frac{20}{21}$$1$