Won't you...? ～ませんか？
Why don't we study Japanese grammar?
ok. Since we have the above construction (using a negative to suggest doing something) in English, this grammar point isn't too difficult to grasp.
1) ~masu verb - masu + masen ka
dokoka ikimasen ka.
Why don't we go already?
[notice I have the English as 'we.' It could be 'you' if you are angry at the person and wish him to leave...]
eiga o mimasen ka .
Why don't we see a movie.
nanika nomimasen ka.
Wouldn't you like to drink something?
[In this case you are asking someone individually if they would like something to drink. ]