A sufficient condition on operator order for strictly positive operators

Let $A_1$, $A_2$, $\mathrm{.}\mathrm{.}\mathrm{.}$, $A_k$ be strictly positive operators on a Hilbert space. This note is to show a sufficient condition of $A_{k}\geq A_{k-1}\geq\geq A_{3}\geq A_{2}\geq A_{1}$, which extends the related result before.