1. The problem statement, all variables and given/known data For the series x^n - x^(n-1) - x^(n-2) ... - x^(0) the roots seem to be x = 2 and the circle around the complex plane with radius i or 1 I'm not sure how you would say it as n approaches infinity. Here's an image of the roots where n = 15. http://www.wolframalpha.com/input/?...x^11-x^10-x^9-x^8-x^7-x^6-x^5-x^4-x^3-x^2-x-1 2. Relevant equations 3. The attempt at a solution http://www.wolframalpha.com/input/?...x^11-x^10-x^9-x^8-x^7-x^6-x^5-x^4-x^3-x^2-x-1 This is beyond me but it really intrigued me as to why the roots seem to create a circle in the complex plane. I have almost complete Calculus AB and have read a lot into other advanced topics but I have no idea how I would go about finding all of the roots for this infinite series or why they seem to create a circle. I was hoping someone would as I thought it was pretty cool.