其中句子中keeping前的for为介词,介词后动词用ing形式,所以要用keeping.介词后一定要用动词ing形式句意为:我很抱歉让你等待很长时间,而keeping是修饰前面的sorry的，for keeping表示保持自己一直的歉意（别人等我很久）的意思。也可以不用keeping，用其他的词，
I am terribly sorry to keep you waiting for a long time.
I'm sorry to keep you waiting for such a long time.

I am sorry to have kept you waiting for a long time
I'm awfully sorry to have kept you waiting for a long time
都可以的