The narrator of "The Tell-Tale Heart" by Edgar Allan Poe repeatedly tries to prove to the reader that he is sane, but his very attempts to prove his sanity in fact undermine his claim. Sane people don't normally spend a great deal of time insisting that they are sane; the only people who need to prove their sanity are those whom others might consider insane.
The narrator claims that his mental acuity is evidence of sanity, offering as evidence the care with which he plotted the murder and the cleverness of his design. He also argues that his patience in planning and executing the murder was a sign of sanity. He describes how he would open the door of the old man's room and shine a single ray of light on the man's eye using a specially designed lantern as evidence of his sanity. Finally, he describes his clever scheme for concealing the body as evidence of sanity.