Hoi guys,

suppose we have $\displaystyle p_{k+1}\geq p_k^9+9p_k^8(1-p_k)$

I'd like to show that $\displaystyle p_k\to 1$ as $\displaystyle k\to\infty $ if $\displaystyle p_0>0.968...$

Now, this seems quite obvious maybe...as $\displaystyle p_{k+1}>p_k$ if $\displaystyle p_0>0.968$

But how can we see $\displaystyle p_k\to 1$?