Answer: The right answer is the C) "This paper will show you..."
Explanation: Just to elaborate a little on the answer, it can be added that informal language and colloquialisms, which can be used in a casual conversation, should be avoided in essays, which are formal by definition. Much like we, and to a lesser extent I, the word you should not be used in an essay, since, although it may seem that you are not addressing a specific person (after all, you is often used in spoken English to generalize), the reader can get distracted and confused. It is preferable to use the indefinite one, or, alternatively, you can also say "this paper will show the reader...".