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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!

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    $b_2=e^{-250}$, which is a number very very close to $0$, then $b_3=e^{b_2}$ would hence be a number very very close to $1$, then $b_4$ would be very very close to $e$, and then you start having towers of $e$, which explode very quickly2012-03-20

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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 $b_n \rightarrow \infty$