I'm an undergraduate math major (just completed my second year), and I had applied for a summer school (online due to the pandemic) in one of my interest areas. I have taken two courses in this area with the same professor (one of them was a graduate course if it matters). I did pretty well in both courses, i.e. got As.
I requested the aforementioned professor to write me a recommendation letter for the summer school, which they gladly did - but unfortunately, I did not get accepted (the school has about a 14% selection rate).
Should I inform the professor (i.e. my letter writer for this program) that I have been rejected? Do they already know, in which case I don't have to do anything? Do programs typically inform about acceptance/rejections to letter writers too, or do they only inform the applicants? This is my first time applying to a summer school, so I don't really know how this works.
Also, given this experience, would it make sense to ask the same professor again to write me a letter for graduate school applications? I don't know what went wrong - (i) if the professor didn't write me a strong enough letter, or (ii) if I really wasn't good enough to get into the program. It's probably the latter, but given the probabilistic nature of this dilemma, I really don't know what conclusion to draw. Moreover, graduate school applications are going to be far more important than applying to a summer program, so I should know what to do.
Please let me know in case any clarifications are needed. Thanks a lot!