Verb, Masenka
Won't you do
for example
トラ君明日あそびに行きませんか
tora kun, ashita asobini ikimasenka?
hey tora, tomorrow will you come to my house.
ひまだったら、図書館へ行きませんか。
himadattara, tosyokan he ikimasenka.
if you have free time, will you (with me) going to library
明日花火に行きますか
ashita hanabi ni ikimasenka
Won't you going to see fireworks tomorrow ?
this usage is for inviting some one to do some thing, rather than just asking theri intentions.