$\sum_{k=1}^{180^\circ}\cos\left(\frac{2\pi}{k}\right)$
5080
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
26370
Consider convergence of series: $\sum_{n=1}^{\infty}\sin\left[\pi\left(2+\sqrt{3}\right)^n\right]$
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
139430
How to prove that $\sum_{n=1}^{+\infty}\frac{1}{n^2+1}=\frac{-1+\pi \coth (\pi)}{2}$?
134610
Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
25967
Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$
84557
Using right-hand Riemann sum to evaluate the limit of $ \frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$
108694
Efficient computation of $\sum_{i=1}^{i=\left \lfloor {\sqrt{N}} \right \rfloor}\left \lfloor \frac{N}{i^{2}} \right \rfloor$
15045
Proving $\sum\limits_{l=1}^n \sum\limits _{k=1}^{n-1}\tan \frac {lk\pi }{2n+1}\tan \frac {l(k+1)\pi }{2n+1}=0$
123264
Showing $\sum\limits_{cyc}ab\le\frac14\left(\sum\limits_{cyc}a\right)^2$
150822
Finding $\sum_{k=0}^{n-1}\frac{\alpha_k}{2-\alpha_k}$, where $\alpha_k$ are the $n$-th roots of unity
21855
Prove $\sum_{n=1}^{\infty}\arctan{\left(\frac{1}{n^2+1}\right)}=\arctan{\left(\tan\left(\pi\sqrt{\frac{\sqrt{2}-1}{2}}\right)\cdots\right)}$
56365
Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
72403
Given $A+B+C=180^{\circ}$, find value of $\tan A\cdot\tan B+\tan B\cdot\tan C+\tan A\cdot \tan C-\sec A\cdot\sec B\cdot\sec C$
134633
How to sum this series for $\pi/2$ directly?
37007
Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
116019
Find the limit $\lim\limits_{n\to \infty}\sum\limits_{k=1}^{n}\left(\frac{k}{n^2}\right)^{\frac{k}{n^2}+1}$