Take 10 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
If you have more questions, feel to ask then on the forum.
Question
We denote by
a fixed natural integer.
We define a sequence
by:
Find the limit of sequence
Indice
Set
then do a Taylor-expansion of order 1 of
and get back to a form
Solution
We notice that for any non zero natural integer
is a real positive number and we set
This results in the fact that sequence
converges towards
therefore, by continuity of the exponential application, sequence
converges towards
