The type of human cell that doesn't have a nucleus is a red blood cell, also known as an erythrocyte.

Here's why:

* Function: Red blood cells are responsible for transporting oxygen throughout the body.

* Lack of Nucleus: To maximize their oxygen-carrying capacity, red blood cells eject their nucleus and other organelles during development. This allows them to pack more hemoglobin, the protein that binds to oxygen.

* Limited Lifespan: Without a nucleus, red blood cells cannot repair themselves or replicate. They have a lifespan of about 120 days, after which they are broken down by the spleen.