1. I appreciate your sending the papers.
Here's why:
* "Sending the papers" is a gerund phrase acting as the object of the verb "appreciate." It's a concise and elegant way to express the action.
* "You papers" is grammatically incorrect because it's missing a verb. It would need to be "Your sending the papers" or "You sent the papers" to make sense.
Therefore, option 1 is the correct and grammatically sound sentence.