Why $\zeta(-2) $ is not $\sum_{n=1}^{\infty}\frac{1}{n^{-2}}$?
4340
Why does $1+2+3+\cdots = -\frac{1}{12}$?
37802
Why doesn't $\sum_{n=1}^\infty \frac{1}{n^{1+\frac{1}{n}}}$ converge?
115816
Grandi's Series; tends to $1/2$, but why is this considered a valid sum?
92754
Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$
150148
Sum of $\sum^\infty_{n=2} \frac{1}{\ln{(n!)}}$
154544
Prove that $ \sum_{n=0}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}=\frac{z}{1-z} $
158737
What is the value of the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n^2}$?
111705
Why does $\frac{1+t}{(1-t)^3}=\sum_{n=0}^{\infty}(1+n)^2t^n$
53658
Find the sum series $\sum_{n=1}^{+\infty} \frac{(-1)^{n-1}(2n-1)}{2^{n-1}}$
138516
$\sum (-1)^{n+1}\log\left(1+\frac{1}{n}\right)$ convergent but not absolutely convergent
33441
Proof that $\sum\limits_{k=1}^\infty\frac{a_1a_2\cdots a_{k-1}}{(x+a_1)\cdots(x+a_k)}=\frac{1}{x}$ regarding $\zeta(3)$ and Apéry's proof
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
39524
Integral Representation of the Zeta Function: $\zeta(s)=\frac1{\Gamma(s)}\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$
127267
Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
6436
Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
132182
$\sum_{n=1}^\infty \sum_{m=1}^\infty\frac{1}{(m+n)^2}$
136602
Why is $\int_1^{\infty}(1/x^2)\,dx$  less than $\sum_{n=1}^{\infty} 1/(n^2)$?