Problem
====================
Let
with the following recursion relation
Start with the index n = 1 and group to the index n = 20. How can you tell that the results are incorrect and at what index n?
Attempt
====================
I do not think that the results can be incorrect; I think it is true for all indices.
First, I integrate
using integration by parts (I forgot how to do the "evaluate from/to" symbol in Latex so I used a bracket)
Simplify to get
Since
, then
Thus,
Shouldn't this be true for all indices n? I wrote a MATLAB script that computed
at all indices and the results look fine.
Thank you for reading.