People will probably live on average to be over 1000, maybe 10,000 because people will only die from accidents. Science will advance at a faster rate because we don't have to spend the first 25 years or so of life on primary education. The next problem will be that without new generations, human evolution will be at a standstill. But, perhaps not totally. If we can direct our own evolution using simulation and very limited reproduction, say with the average age of a parent being about 1000 years or more, then perhaps we can still find ways to advance as a species. We might be able to grow new bodies and perhaps even new brains for ourselves. When we want to alter our DNA, we could somehow become chimeras for a period of time until the old DNA is completely replaced by the new upgraded DNA. In this way, our species gets all the evolutionary benefits of death without actually having to die.
The only problem with this theory is assuming that humans are mentally ready to live 1000 years or more.
Forget Alzheimer's or dementia for a minute (no pun intended). And pretend we cure cancer (all of them, somehow).
What makes you think grandpa will ever be mentally ready to stave off natural pessimism or cynicism for a few hundred years or more?
Perhaps the most likely answer to that is VR, but then that brings into question just exactly what kind of "world" we would be "living" in at that point.