Originally Posted by
pseudonym Hi can someone please help me with the following please:
Find the generating functions for the following sequences, express them in a closed form, without infinite sums:
(i) 1,2,1,4,1,8,1,16,1,...
(ii)1,1,0,1,1,0,1,1,0,...
This is what I have so far:
(i)i've written it as 1 + 2^1*x^1 + (2x)^0 + 2^2*x^3 + (2x)^0 + 2^3*x^5 +...
if the sequence didnt have all the ones inbetween, I think i'd know how to do it, using differentiation on (1/(1-x)) multiplied by something. But I'm not sure how to incorporate the ones into the sequence...
Thank you for your time