If you look at computer chess it improved steadily, there was a bit of a fuss when it beat Kasparov, then it kept going. People still play each other at chess much as before.

I figure it'll be like that with general intelligence - bit of as fuss as AI overtakes but humans will keep on humaning, making things, competing for status. Maybe like Jeeves and Wooster with us as Wooster and the AI as Jeeves. Most of their activities didn't bring much value apart from keeping people busy. AI will probably keep improving a few IQ points a year, not exploding but gradually getting pretty good.

For me the more interesting sci-fi is the merge / immortality stuff, curious how that goes.