## Minimizing by Mathematica

Dear Friends,

I want to minimize the function $j\beta^{j-1}$, where $j\in\mathbb{N}$ and $\beta\in(0,1)$ by using Mathematica.
I have tried some codes but all failled.
One of them is
Code:
FindMinimum[j*\[Beta]^(j - 1),
j \[Element] Integers && 1 <= j && \[Beta] < 1 && \[Beta] > 0, j]
What should be the right code?