Define the sequence by and Evaluate
How can people ( is that you ?) find out this this expression/series for irrational numbers ?
we can see that the series converges so quickly !
for this problem ,
I use a quite complicated method , is there any method better than mine ?
Go through it !
the general term of the seqence is
so the product of first terms is
the series can be written in this form :
To evluate this series , we just need to create next to the series .
or an elegant-appearance
the fifth term is about , wow
I have consider another method but got stuck somewhere ...
so i obtain a functional equation
and i know is a one of the solution
so i let
i found that
but the problem is here :
is also the solution but how do we get the exact value of ? ( )