A sentence-ending expression used to ask for agreement or to express exclamation/confirmation — 'isn't it?' or 'don't you think?' (colloquial).
この景色は本当に美しいじゃないか。
This view really is beautiful, isn't it?
そんなことを忘れるなんて、信じられないじゃないか。
To forget something like that — it's unbelievable, isn't it?
もう少し頑張れば合格できるじゃないか。
If you try a little harder, you can pass, can't you?
Used after the volitional form of a verb to propose or urge action: 'let's ...' or 'why don't we ...' (often somewhat forceful or rhetorical).
皆で力を合わせてやろうじゃないか。
Let's all join forces and do it.
ここで諦めるのはやめようじゃないか。
Let's not give up here.
一度きりの人生、挑戦してみようじゃないか。
It's a once-in-a-lifetime chance — why not give it a try?