For every n E N* we consider the function fn : (1; 0) → R fn(x) = In" z show that fn(x) < E (1, 0) and Vn e N*
$$
\begin{array}{l}
\text { For every } n \in \mathbb{N}^{*} \text { we consider the } \\
\text { function } f_{n}:(1 ; \infty) \rightarrow \mathbb{R} \\
\quad f_{n}(x)=\frac{\ln ^{n} x}{x} \\
\text { sMow that } f_{n}(x) \leqslant \frac{n^{n}}{e^{n}} \forall x \in(1, \infty) \\
\text { and } \forall n \in M^{*}
For every $n \in \mathbb{N}^{*}$ we consider the
function $f_{n}:(1 ; \infty) \rightarrow \mathbb{R}$
$\quad f_{n}(x)=\frac{\ln ^{n} x}{x}$
sMow that $f_{n}(x) \leqslant \frac{n^{n}}{e^{n}} \forall x \in(1, \infty)$
and $\forall n \in M^{*}$
\end{array}
$$
please check the attached image to see the problem clearly,I have attached a screenshot for the output of the above latex code.
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