Sum $1+(1+x)^2+(1+x+x^2)^2+\cdots+(1+x+x^2+\cdots+x^{N-2})^2 $ Is there a way to find the sum the following series:
$$1+(1+x)^2+(1+x+x^2)^2+\cdots+(1+x+x^2+\cdots+x^{N-2})^2 \text{ ?}$$
Any ideas ? Perhaps someone knows already the result..
Thank you in advance for your time.

Hint: Let $S$ be your series, and consider $(1-x)^2 S$. What happens to each term when you distribute and simplify?
