Find $\sum_{i=1}^{n-1}\frac{1}{2-a^i}$ if $1,a,a^2,...,a^{n-1}$ are the n$^\text{th}$ roots of unity
54015
Series involving complex roots: $\frac{1}{2-a_1} + \frac{1}{2-a_2} + \dots + \frac{1}{2-a_{n-1}} = \frac{(n-2)2^{n-1}+1}{2^n - 1}$
138313
How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
91496
If $x_1,x_2,\ldots,x_n$ are the roots for $1+x+x^2+\ldots+x^n=0$, find the value of $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$
74120
Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
11664
If $a_0+\frac{a_1}{2}+\dots + \frac{a_n}{n+1}=0$ then $a_nx^n+\dots + a_0$ has a root in $[0,1]$
111805
If $a_{1}=1$ and $a_{n+1}=1+\frac{n}{a_{n}}$, then $a_{n}=\sqrt{n}+\frac{1}{2}-\frac{1}{8\sqrt{n}}+o\left(\frac{1}{\sqrt{n}}\right)$
17056
How to find answer to the sum of series $\sum_{n=1}^{\infty}\frac{n}{2^n} $
113237
Find the sum of the roots of the floor equation
42165
Complex numbers and Roots of unity
18796
How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$?
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
68725
Find expression for : $ S_n =\sum_{i=1}^{n} \frac{i}{i^4+i^2+1} $
52987
$\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
89705
How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?
136066
Find the sum $\sum _{n=1}^{\infty }\left(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n}\right)$
24000
Roots of Sum of Two Polynomials (with Known Roots)
69067
Principal $n$th root of a complex number