That's just confusion about discount rates.
Money in the future is worth less than money in the present, so an infinite sequence can have a finite sum when it's priced in today's money.
Money in the future is worth less than money in the present, so an infinite sequence can have a finite sum when it's priced in today's money.
If the world is ending tomorrow, then much less. If we discover immortality tomorrow, then much more.
I'd suggest that discovering immortality might have the opposite effect, it would only bring more uncertainty about the future.