Proving this sum is irrational
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
31867
Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational
17930
Please explain this step in proving the square root of 3 is irrational
109953
How to prove that $\sqrt 3$ is an irrational number?
55777
A tricky sum to infinity
128298
Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$
138446
Proving that there exists an irrational number in between any given real numbers
91744
Proving sum of sines is periodic when ratio of their frequencies is rational using differentation
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
31744
Proving that there is an irrational number between any two unequal rational numbers.
85626
prove $\sum_{i=1}^{n}(x_i-\bar{x})^2\lt\sum_{i=1}^{n}(x_i-a)^2$
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
16143
How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
67752
Show that $\sum_{n = 1}^{+\infty} \frac{n}{2^n} = 2$