won't you have some tea?

not necessarily.
Do you not want a coffee?

Yes, it's an invitation, 99.9% of the time, when used as you describe.

Would you like some tea? is also an invitation. Won't you have some tea? carries a sense that the person asking believe you would like some.

Won't you sit down? is an invitation to sit.

Etc.

Can you help me by giving an example in which there is this sentence: "Won't you have some tea?

Oh, hello, Mrs. Smith. I didn't expect that you would be able to come by to see me so soon. As you can see, I was just sitting down for some tea and cookies. Won't you have some tea with me?

I'm wondering if it is an invitation why is it not "Will you have some tea?" but "Won't you have some tea?" Why the negative form is used here?

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Minhuoc
I'm wondering if it is an invitation why is it not "Will you have some tea?" but "Won't you have some tea?" Why the negative form is used here?

Compare with:
http://tinyurl.com/pdhjp
where it is mentioned that:
"won't you" is seen by some as more urgent than "will you"

Won't you is more insistent and pleading than Will you or Would you like to.
The emotional meaning of Will you is neutral: Yes or no, do you want some tea?
The emotional meaning of Won't you is coaxing and encouraging. It expects a Yes answer.

In my opinion, Won't you is an expression borrowed from the tag question i

Surely) you will have some tea, won't you?


Um....I never thought of it this way.....

It makes a lot of sense.....