Sum of Legendre symbols: $\sum _{n=1}^p \left(\frac{an+b}{p}\right)=0$
48482
Legendre symbol: Showing that $\sum_{m=0}^{p-1} \left(\frac{am+b}{p}\right)=0$
16967
Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$
36023
Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$
4327
proving $\left(1+\frac 1n\right)^{n} = 1 + \sum_{k=1}^n \{\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn)\}$ using the binomial theorem
128608
Closed form for the series $a+a^p+(a^p)^p+\dots$
25507
Find the limit of $\sum\limits_{k=1}^n\left(\sqrt{1+\frac{k}{n^2}}-1\right)$
78033
Evaluating $\prod_{n=1}^{\infty}\left(1+\frac{1}{2^n}\right)$
150200
finding $\lim_{n\rightarrow\infty}\sum_{r=1}^{n}\arctan\left(\frac{2r}{1-r^2+r^4}\right)$
129574
Sum over all residues is zero
123264
Showing $\sum\limits_{cyc}ab\le\frac14\left(\sum\limits_{cyc}a\right)^2$
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
44970
Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
148970
How to calculate such sums of Legendre symbols?
138704
when p is sum of two square integer, prove (a/p) which is legendre symbol = 1
69084
What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
62463
A pencil approach to find $\sum \limits_{i=1}^{69} \sqrt{\left( 1+\frac{1}{i^2}+\frac{1}{(i+1)^2}\right)}$
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial