Evaluating $\sum\limits_{k=0}^n\cos(kx)$ and $\sum\limits_{k=0}^n\sin(kx)$ without Complex Numbers
5080
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
60104
Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
56365
Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
70742
Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital
134311
How to determine equation for $\sum_{k=1}^n k^3$
107386
Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
64581
How to find the sum $\sum\limits_{k=1}^n (k^2+k+1)k!$?
114911
Evaluate $\sum_{k = 0}^{n} {n\choose k} k^m$
17713
What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
132613
Testing the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{k + \cos{n}}}$
2302
Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)
114031
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
34637
Evaluating $\sum\frac{\sin(n)}{n^a}$