another proof of Bernoulli’s inequality

For fixed $x>0,\ x\neq 1$ the function

w_{x}(r)=\int_{1}^{x}t^{r-1}dt=\begin{cases}\frac{x^{r}-1}{r}&r\neq 0\\ \log x&r=0\end{cases}

w_{1+x}(r)>(<)\ w_{1+x}(1)

Title	another proof of Bernoulli’s inequality
Canonical name	AnotherProofOfBernoullisInequality
Date of creation	2013-03-22 15:45:43
Last modified on	2013-03-22 15:45:43
Owner	a4karo (12322)
Last modified by	a4karo (12322)
Numerical id	7
Author	a4karo (12322)
Entry type	Proof
Classification	msc 26D99