The narrator attempts to prove himself sane by recounting the actions he took before killing the old man. He believes that his planning and his foresight prove that he is not mad because "madmen know nothing".
He tells the reader that he "was never kinder to the old man than during the whole week before [he] killed him." He then goes on to explain how he would sneak into the old man's room and shine his lantern. He would do this with extreme caution, which he believes, once again, to prove his sanity. The irony is that these obsessive traits do more to show the opposite.