I don't remember how to do math
Prove that $\sum_{j=1}^{k} r_{j}{\log p_{j}} -\sum_{j=1}^{k} r_{j}{\log r_{j}} <=0$
Can I just put all expressions in one sum symbol, use log probability $\log(p_{j})-log(r_{j})=log(p_{j}/r_{j})$. Then we use Jensen Inequality to get ${\log(}\sum_{j=1}^{k} r_{j}*{\ p_{j}/r_{j}} )$ We simplify both $r_{j}$ and we get ${\log(}\sum_{j=1}^{k} p_{j})=0$ (since I think $\sum_{j=1}^{k} p_{j})=1$
Is that the correct way to do things?