Show $\left(1+\frac 1 x\right)^{x} < e < \left(1+\frac 1 {x}\right)^{x+1}$
95415
proof relating to limit definition of e
128128
Show that $\lim_{n \to \infty} \left(1+\frac{a_n}{n}\right)^n= e^a$ when $a_n \to a$
107058
Prove that $E(X\ln X)\le E X E\ln X$
72506
An example s.t. $E(E(X|\mathcal F_1)|\mathcal F_2)\neq E(E(X|\mathcal F_2)|\mathcal F_1)$
99821
Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.
117370
$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
127291
Show that $\left( \frac{q}{p} \right) \equiv q^{(p-1) / 2} \mod p$, where $\left( \frac{q}{p} \right)$ is the Legendre Symbol
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
138107
Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
6100
Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
147977
Evaluate $\int_0^1\left(\frac{x-1}{x+1}\right)^n\frac{1}{\ln x} \,dx$
118204
Finding limit of $\left(1 +\frac1x\right)^x$ without using L'Hôpital's rule.
78033
Evaluating $\prod_{n=1}^{\infty}\left(1+\frac{1}{2^n}\right)$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
69653
Inequality $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$