Compute $\sum\frac1{2-A_k}$ for $(A_k)$ the $n$th roots of unity
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 $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$
41312
Question on primitive roots of unity
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
54015
Series involving complex roots: $\frac{1}{2-a_1} + \frac{1}{2-a_2} + \dots + \frac{1}{2-a_{n-1}} = \frac{(n-2)2^{n-1}+1}{2^n - 1}$
129734
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
89367
Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
102942
Compute the sum $\sum_{k=1}^{\infty}k^mz^k$ where $|z|<1$
12812
Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
113237
Find the sum of the roots of the floor equation
110416
Sums of roots of unity
106552
Find the sum of $\sum \frac{1}{k^2 - a^2}$ when $0<a<1$
49851
when the sum of some fractions be $1$
22524
Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
126105
Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
124229
Simplify $\sum_{k=0}^{\infty} x^ky^{\frac{k(k+1)}{2}}$
134610
Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$