How to find the value of $\sum\limits_{n=0}^\infty r^n \sin(n\theta)$?
114031
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
158737
What is the value of the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n^2}$?
32866
How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
4638
What is the value of $\lim_{n\to \infty} \sum_{j=n}^{4n} {4n \choose j}\bigl(\frac{1}{4}\bigr)^{j} \bigl(\frac{3}{4}\bigr)^{4n-j}$?
17019
Show that: $\lim\limits_{r\to\infty}\int\limits_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$
56961
Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$
43368
How to prove $\sum\limits_{n=1}^\infty\frac{\sin(n)}n=\frac{\pi-1}2$ using only real numbers.
54661
How to find the sum $\sum\limits_{n=1}^{\infty}\frac{1}{n!(n^4+n^2+1)}$
117583
Why does $\sum_{n=0}^\infty (\sin{\frac{1}{n}})(\sinh{\frac{1}{n}})(\cos n)$ converge
22657
How to find the sum of the infinite series?
8626
The limit of a sum (a Riemann sum?)
125087
Evaluate the limit of ratio of sums of sines (without L'Hopital): $\lim_{x\to0} \frac{\sin x+\sin3x+\sin5x}{\sin2x+\sin4x+\sin6x}$
5433
Finite Sum $\sum\limits_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}$
130241
What is the Convergence Radius and Domain of $\sum\limits_{n=0}^\infty \frac{1}{2^{n}} z^{2^n}$?
143207
What is $\sum\limits_{i=1}^n \sqrt i\ $?
157972
Find a closed form expression for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$
112772
Is the series $\sum \limits_{n=1}^{\infty} \sin(n^2)$ convergent?