Should I inform my letter writer about a summer school rejection? Should I ask the same professor to write me a letter for grad school? 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!
Yes, you should tell them and yes, it makes sense to ask them again. Likely the rejection wasn't due to the letter they wrote, but to the level of competition for positions in the program.
But, in general, your letter writers should be people who know you and your work well and can make a confident prediction of your future success. I assume that this is one of those people. And informing them might get you an even stronger letter.
Note, of course, that the standards are different for a summer program and a graduate program. And the competition won't be less. Apply to universities that fall over a range of rankings so that you have a better chance of acceptance. If you apply only to top ranked small schools you greatly lessen your chances.
While a summer program has a fixed number of &quot;seats&quot;, applying to several schools opens the number of possibilities.