Prove that$\frac{\Gamma(n+1,n+1)}{\Gamma(n+1)}/{\frac{\Gamma(n,n)}{\Gamma(n)}}$ is decreasing function.
35091
How can I prove this sequence is decreasing?
105145
Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
37489
Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
112512
How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?
126736
Show that $\lim_{\epsilon\to0^{+}}\frac{1}{2\pi i}\int_{\gamma_\epsilon}\frac{f(z)}{z-a} \, dz=f(a)$
68385
Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
9046
Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
141837
Proof of $\sup\{ (n!)^{(\frac{1}{n})}| n ∈ N\} = +∞?$
48651
Prove that $\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}$ for positive $p$ and $q$
157898
Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$
145632
Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
75279
Reversing the $T(n) = \frac{n(n+1)}{2}$ formula
102414
$\lim_{n \to \infty} (\frac{(n+1)(n+2)\dots(3n)}{n^{2n}})^{\frac{1}{n}}$ is equal to :