Wikipedia:Reference desk/Archives/Mathematics/2018 November 16

= November 16 =

Limit of real root of a polynomial
Let $$f_n(x) = \sum_{k=0}^{n} x^{2^k - 1}$$. It's easy to see that there is always 1 real root, call it $$r_n$$. Does $$\lim_{n \to \infty} r_n$$ have a closed form? Is there anything interesting to say about it? Numerically it is approximately -0.658626754300164. 98.190.129.147 (talk) 17:43, 16 November 2018 (UTC)
 * Apparently the number is mentioned in this article. It's got a pay wall though. --RDBury (talk) 22:03, 16 November 2018 (UTC)
 * That article credits the sum to . Unfortunately neither says much more about the real zero than you've figured out already (one has a proof of convergence), they're both mostly about complex zeros of $$f_n(x)$$. 78.0.230.255 (talk) 00:50, 17 November 2018 (UTC)