I trust you will pardon me for——

I write to apologize for my failure to——

I hope you will forgive me when I tell you that——

I am sorry I could not do as I had promised to do

I am very much mortified to find that——

Trusting you will forgive my great carelessness

I hope you have not suffered any inconvenience from——

Hoping you will pardon the——

I am afraid you will accuse me of rudeness, but I——