1+2+3+4+… = -1/12, Ramanujan's Sum 📺
1+2+3+4+... = -1/12
wow. How is it possible?
that's called Ramanujan's sum.
you can learn it from the first 15 min of John Baez lecture
- https://youtu.be/vzjbRhYjELo
- John Baez on number 24
- (quantum mechanics, string theory)
this is quite amazing, touching on several things. See:
- Ramanujan summation
- 1 + 2 + 3 + 4 + …
- http://math.stackexchange.com/questions/39802/why-does-123-dots-1-over-12
on a separate note, the rest of Baez's video is also extremely interesting. It introduces you to concepts of string theory, quantum mechanics, spinor theory.
- i don't understand it well, will take days to digest it all.
- But, if you have trouble reading the above references, here's a handwaving explanation.
- Basically, when given a sum of infinite sequence, the most important thing to
- When you add a infinite sequence, the first question is whether
- sequence converge or diverge. Diverge means the number will get bigger
- and bigger.
- For some sum, you can find out a range of values when the sum will converge.
- For example, this sum
Sum[n^(-s),{n,1,∞}]
- (called Riemann zeta function), will converge when
s ≻ 1.
- For example, if
s=2, we have1/1^2 + 1/2^2 + 1/3^2 + …and one can find out that the value isπ^2/6. - when s is less or equal to 1.
- Tao's latest post,
- https://plus.google.com/114134834346472219368/posts/ZuJDv3daT9n
- Ramanujan's formula
- 1+2+3+4+... = -1/12 (1)
- i completely don't understand. Can any point to references to this particular series?