Thank you vs. Thanking in advance

[Jupiter]

Hi teachers,

After doing the free quizzes about formal language, I got one question to be answered.

............I look forward to hearing from you.
1/ Thank you
2/ Thanking in advance

The answer is the second one, Thanking in advance.
Why not Thank you in advance or Thanks in advance?

Jupiter

[Mister Micawber]

.
I don't know; it may be a typo. The sentence structure you have presented does not allow of either answer.

In any case, I think the -ing form should be avoided as effete.
.