Help me please with this question:
Let $b_{1}=-250$ and for all $n\geq 1$ $b_{n+1}=e^{b_{n}}$.
Prove that sequence $b_{n}\rightarrow \infty $
Thanks!
Help me please with this question:
Let $b_{1}=-250$ and for all $n\geq 1$ $b_{n+1}=e^{b_{n}}$.
Prove that sequence $b_{n}\rightarrow \infty $
Thanks!
We have the convexity inequality $\forall x \in \mathbb{R} $ , $e^x - x \geq 1 $ . By induction you get $b_n \geq n + b_0$ and so $b_n \rightarrow \infty$