Prove ln(1+1/x)-(x+1)^-1 is always positive [solved]
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
98768
Prove $\left(1+\frac{x}{n}\right)^n < e^x$, where $x$ is any positive real number and $n$ is any positive integer.
33097
Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
72693
Prove: $\lim_{x\to\infty}x^{2/3}((x+1)^{1/3}-x^{1/3})=1/3$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
18156
Find $\lim_{x\to \infty} \ln(x+1)/(\ln(x))$
149889
Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$
107765
Prove that there exists two roots in $[-1,1]$
52108
how to prove Exponential is strictly positive?
89175
Proof of $(a+b)^{n+1}$
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
129331
Prove that $|x^p - y^p| \le p|x-y|(x^{p-1} + y^{p-1})$ provided that $1 \le p \lt \infty$ and $x, y \ge 0$
44328
Prove that $\sum_{k=1} ^ n k^{-1} = \ln(n) + O(1)$
44799
Why is the even root of a number always positive?
88328
Proof of $1+x\leq e^x$ for all x?