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

Construction:
1) ~masu verb - masu + mashou

どこか行きませんか dokoka ikimasen. 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...]

映画を見ませんか eiga o mimasen ka . Why don't we see a movie.

何か飲みませんか 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. ]