Is $\sum_{n=1}^{\infty} \frac{1}{\operatorname{lcm}[1,~2,~\ldots,~n]}$ irrational?
31867
Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
145798
Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
62504
Is there any known relationship between $\sum_{i=1}^{n} f(i)$ and $\sum_{i=1}^{n} \dfrac {1}{f(i)}$
1098
Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?
120743
For Riemann sums involving square roots, why do we let $c_{i} = \frac{i^{2}}{ n^{2}}$?
80683
Convergence of $\sum_{n=1}^\infty\frac{1}{n} [1+\frac{1}{\sqrt{2}}+.....+\frac{1}{\sqrt{n}}]$
137249
find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$
109718
Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?
70867
Is $\sum_{n=1}^\infty\frac{(-1)^n}{n\log^2(n+1)}$ absolutely convergent?
5817
Does the series $\sum \limits_{n=2}^{\infty }\frac{n^{\log n}}{(\log n)^{n}}$ converge?
59485
Infinite Series: $\sum_{n=1}^\infty \frac{1}{2^nn}$
106028
Sum of $\frac{1}{(2n)(2n+1)}$ from $1$ to infinity
42216
Sum of infinite series $\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}$
63900
Convergent or divergent series: $\sum_{n=1}^{\infty} \sqrt{a_n \cdot a_{n+1}}$?
132351
Is the infinite sum of $2 ^{-n}$ convergent? Why?