Y by
this was given to me by a friend

a nice solution using sandwich is

therefore
= 
ALSO ANOTHER SOLUTION WHICH I WAS THINKING OF WITHOUT SANDWICH BUT I CANT COMPLETE WAS TO USE THE GAMMA FUNCTION
we know


and
for integers,
= 
therefore from the gamma function we get
=
= 

somehow im supposed to show that

all i could observe was if we do L'hopital (which i hate to do as much as you do)
i get
now since
, as
the
which gets us the
form therefore L'hopital came to my mind , which might be a completely wrong intuition, anyway what should i do to find that limit


a nice solution using sandwich is

therefore


ALSO ANOTHER SOLUTION WHICH I WAS THINKING OF WITHOUT SANDWICH BUT I CANT COMPLETE WAS TO USE THE GAMMA FUNCTION
we know


and



therefore from the gamma function we get






somehow im supposed to show that


all i could observe was if we do L'hopital (which i hate to do as much as you do)
i get

now since






This post has been edited 3 times. Last edited by Levieee, Apr 20, 2025, 10:14 AM