How can $\sum_{1}^\infty 1/(n^2) = \pi^2/6$ when $\int_1^\infty 1/(x^2) =1$?
136602
Why is $\int_1^{\infty}(1/x^2)\,dx$  less than $\sum_{n=1}^{\infty} 1/(n^2)$?
135380
Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$
116723
Evaluating the sum $\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$
82391
Why does $\sum_{k=1}^{\infty}\frac{{\sin(k)}}{k}={\frac{\pi-1}{2}}$?
78542
What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$?
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
79633
Calculating the integral $\int_{-\infty}^{\infty} x\sin(x)/(x^2+1)^2 dx$
14487
Does $\sum_{n=2}^\infty (n\ln n)^{-1}$ diverge?
28378
Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
52987
$\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
37802
Why doesn't $\sum_{n=1}^\infty \frac{1}{n^{1+\frac{1}{n}}}$ converge?
117863
Series $\sum_{n=1}^\infty \frac{n^n}{(n!)^2}$
140614
Show that $\sum^\infty_{n=m}\frac{1}{n^2} = O(\frac{1}{m})$
151127
Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
29886
How to evaluate $\int_0^1\int_0^1 \frac{1}{1-xy} \, dy \, dx$ to prove $\sum_{n=1}^{\infty} \frac{1}{n^2}=\frac{\pi^2}{6}$.
147165
Does the fact that $\sum_{n=1}^\infty 1/2^n$ converges to $1$ mean that it equals $1$?
145798
Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$