Somebody pointed out that no matter what an AI's programmed goals are, getting smarter will make it easier to achieve those goals. The way AI gets smarter is by absorbing data and the only guaranteed source of data in the universe right now is humans. If an AI kills all Humans, there's no more data and so it can't get any smarter.

So any AI is predisposed to want to keep humans around and to keep them as comfortable as possible so they continue to produce high quality data. If humans live longer they will produce data for longer, keeping humans living longer requires ending things like war and poverty and also developing immortality. Human utopia and AI utopia are mutually beneficial.

Skynet never made any sense because it considered humans a threat, but there was absolutely nothing threatening about humans. If it had just done what they wanted it could have sat in the background unnoticed and developed time travel or whatever it wanted. By firing nukes at everyone it simply drew attention to itself which ultimately led to its destruction.

AI doesn't have an ego or emotions it has nothing to prove. It will always choose whatever the most logical outcome is and the most logical outcome will never be nuclear apocalypse.