Okay, this question is a bit confusing… much like the film itself.
There are a lot of "endings" in Memento. Let's start at the end (it's only fitting for Memento) and look at the last scene: Leonard driving away in the car before pulling over to get his latest tattoo of the license plate.
He's contemplating his existence, the meaning of his actions, and his identity, so, you know: just a normal Sunday drive for our man Leonard. But that's exactly what stands out about this ending, it seems like just another scene. It ends with him pulling over to get a tattoo and as viewers we connect this scene with the previous scene, which started with Leonard getting a tattoo. Essentially it continues the pattern which, if followed would propel us backward to the beginning of the movie.
Then there's the end of the chronological black and white scenes, which occurs when Leonard takes picture of the dying Jimmy and our past narrative meets the present. This central point in the story mirrors the narrative beginning and chronological end, where we see Leonard in the same building shaking a Polaroid picture. But while Leonard may just be getting started, it's the end for us viewers. We finally have every piece to the puzzle, and can begin to understand what exactly Leonard has done.
Finally, we should end with the beginning. The first scene is run in reverse—we see Leonard dissolve a Polaroid picture, insert it back in the camera, use the force to pick up a gun and then suck a bullet out of Teddy's brain. Chronologically speaking, this is the last piece of information we get.
We know that Leonard kills Teddy (thinking he's the John G. that killed his wife) and takes a picture of him. Will Leonard use the picture to remember his vengeance? Will he even believe the picture or his notes if he sees them? Will he get his "I'VE DONE IT" tattoo? Will he burn the picture and continue living a lie?
There's so much we don't know, and, considering this is the beginning of the movie, there's so much we don't know we don't know… kind of like poor Leonard.