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,....

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,....

anonymous · Answer

looks like a complex variable function!!

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

but really didn't understand

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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