Question

find a closed form for the generating function of each sequence: a) 1,0,-1,0,1,0,-1,0,1.....
b) 0,1,2,3,4,....

Answer 1

looks like a complex variable function!!

Answer 2

no, sorry, a) is 1/1+x^2
b) x/(1-x)^2

Answer 3

I remember he said that that sequence is coefficients of something like 1, 0x, -1x^2, 0x^3,1x^4,0x^5,-1x^6.......

Answer 4

but really didn't understand

Answer 5

ooooh
a) is the binaomial expansion of \((1+x^2)^{-1}\)

Answer 6

we have \[
(1+x)^{-1}=1-x+x^2-x^3+x^4-\ldots\\
\implies(1+x^2)^{-1}=1-x^2+x^4-x^6+\ldots
\]
the second one is the given series.
so, after you expand in the power series, use the binomial theorm.
when you find alternating signs, then it means that there will be \((1+x)^{-1}\) involved

Answer 7

so, whenever seeing the stuff like that, I have to start at ?