A polite negative-question ending used to ask for confirmation or suggest that something may not be the case (e.g., “isn't it…?” / “wouldn't it be…?”).
この道は危険ではありませんか？気をつけてください。
Isn't this road dangerous? Please be careful.
もう閉店してしまっているのではありませんか。
Might it already be closed?
それは少し高すぎるのではありませんか？
Isn't that a bit too expensive?
A polite invitation or suggestion: “won't you…?” or “shall we…?” used to invite someone or make a polite request/command.
週末に映画を見に行きませんか？
Shall we go see a movie this weekend?
コーヒーをもう一杯いかがですか？（＝コーヒーをもう一杯飲みませんか）
Would you like another cup of coffee? (lit. won't you have another cup of coffee?)
この書類に目を通していただけませんか？
Could you please look over these documents?