How to calculate $ \sum_{k=1}^{n} \sin(2k-1)x $?
5080
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
82391
Why does $\sum_{k=1}^{\infty}\frac{{\sin(k)}}{k}={\frac{\pi-1}{2}}$?
115433
Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$
101052
Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
19581
$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$
95673
General formula for $\sin\left(k\arcsin (x)\right)$
100936
What is the sum of this series: $\frac{2}{\pi}\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$
78632
Summation equation for $2^{x-1}$
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
281
How one can prove $\prod_{k=1}^{n-1} (\cos\theta-\cos(k\pi/n)) = 2^{1-n}\sin(n\theta)\csc\theta$?
143428
How to sum $\sum_{x=0}^{N-1} \cos{\left( \frac{2\pi x}{N} \right)}^{2}$?
52278
How to solve $\sum_{k=2}^\infty {\frac{1}{k^2-1}}$
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
146035
Proving $\sum_{x=0}^{n-1} \cos\left(k +x{2\pi\over n}\right) =\sum_{x=0}^{n-1} \sin\left(k +x{2\pi\over n}\right) =0. $
108401
Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
81589
Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$