Generating function for the sequence $(0,0,0,1,2,...,2^{r-3},...)$

Question

Find the generating function for the sequence $(0,0,0,1,2,...,2^{r-3},...)$

I found this question in my notes. I know the generating function for the sequence $a_r$ is $\sum a_r x^r$ but I'm not sure how to apply it in this case.

EDIT: Removed the typo in the sequence.

It is not clear to me what the general term in the sequence is? — copper.hat, Nov 27 '14 at 16:09

score 0 · Answer 1 · answered Nov 27 '14 at 16:14

0

Hint: $$x^3+2x^4+4x^5+8x^6+\cdots = x^3(1+2x+(2x)^2+(2x)^3+\cdots)$$

Do you know a closed form for the part in parentheses to the right?

answered Nov 27 '14 at 16:14

hmakholm left over Monica

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Generating function for the sequence $(0,0,0,1,2,...,2^{r-3},...)$

1 Answers1