I was studying the proof of $e$ number when I noticed something:  Why is the sequence $(1+\frac{1}{n})^{n+1}$ descending? It starts ascending with grater n but in one moment it starts descending? Why is that? On what $n$ this happens?  Edit: Let me try to rephrase the question... How come  that sequence $(1+\frac{1}{n})^n$ rises, but the sequence $(1+\frac{1}{n})^{n+1}$  falls, just because of the one more 1+1/n multiplication (power)?
Given  $$ y_n=\left(1+\frac{1}{n}\right)^{n+1}\hspace{-6mm},\qquad n \in \mathbb{N}, \quad n \geq 1. $$ Show that $\lbrace y_n \rbrace$ is a decreasing sequence. Anyone can help ?  I consider the ratio $\frac{y_{n+1}}{y_n}$ but I got stuck.
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