http://numberphile.com/videos/analytical_continuation1.html
What is the sum of 1 + 2 + 3 + 4 +.......to infinity? Should be infinity right?
Check out this video. It's about 7 minutes long. You do not need to know calculus to follow the logic.
Please share your thoughts about this in the comments section.
I think we should define this sum as equal to 42! Seriously, we can define it to be anything we want, but is there some value which is "reasonable" and "consistent"? I don't like the fact that adding alternating zeros to this infinite sum can change the value.
ReplyDeleteThis seems related to the problem in physics of renormalization, and for this reason is interesting.