Sequences

Well, it can only be decreasing if 1 is the largest number in the sequence. So you need to prove that, given $x_1 = 1$

$x_{n+1} = \frac{x_n}{e^{x_n}} \leq 1 \forall n \in \mathbb{N}$

which is equivalent to the statement that

$x_n \leq e^{x_n} \forall n \in \mathbb{N}$

and there's your hypothesis

Sorry but I don't see how this proves it is decreasing? I see it proves that all terms are less than or equal to 1.




Hmm, so possibly:
Hypothesis is: $e^{x_n}>1$
True for n=1 since e>1

Then assuming it's true for n,
$x_n\geq \frac{x_n}{e^{x_n}}=x_{n+1}$
Which shows it's decreasing.


It seems so simple now! Thanks.

It seems so simple now! Thanks.

No problem Rayquaza, us dragon's got to look out for each other

Charizard isn't a dragon mate (unless he holds Charizardite X)You're just pretending to be a Pokemon.

Exactly. So I am a dragon now

Lmao you know more about Pokémon than me : o. Do you play/watch it still or nah?