Sum of all residues of $\frac{P(z)}{Q(z)}$ is zero
129574
Sum over all residues is zero
21791
Show that $\sum\limits_{k=1}^\infty \frac{1}{k(k+1)(k+2)\cdots (k+p)}=\frac{1}{p!p} $ for every positive integer $p$
12966
Riemann Sums proving function identically zero
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
84167
Regarding the sum $\sum_{p \ \text{prime}} \sin p$
35821
Infinitely many primes for quadratic residues
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
65407
Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
55621
Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
78473
Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
63427
A Problem with Residue Theorem
141390
Closed form for $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2+a^2}$
154544
Prove that $ \sum_{n=0}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}=\frac{z}{1-z} $
102942
Compute the sum $\sum_{k=1}^{\infty}k^mz^k$ where $|z|<1$
104904
Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.