1 - 12 =
-11
People also ask
What is the 1/12 theory?
It says that when you add up all the natural numbers. 1+2+3+4+... then the answer to this sum is -1/12. The idea featured in a Numberphile video (see below), which claims to prove the result and also says that it's used all over the place in physics.
Why is sum to infinity 1/12?
It might seem counterintuitive, but the assertion that the sum of natural numbers up to infinity equals -1/12 is based on a particular way of assigning values to divergent series, known as Riemann zeta function regularization.
Can you add 1 to infinity?
If you add one to infinity, you still have infinity; you don't have a bigger number. If you believe that, then infinity is not a number.
Is the Ramanujan summation true?
“Ramanujan summation” is a way of assigning values to divergent series. As such, it isn't true or false, just defined (or not, as the case may be). This particular case really does “work”. However, the left-hand side should say that it's a Ramanujan summation, not a regular “sum of a series”, and it doesn't.
The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯. The parabola is their smoothed asymptote; its y-intercept is −1/12.
Oct 2, 2023 · The first and most important thing is that when you have infinite sums, they only have value if they approach a limit. Take the sum 1 + 1/2 + 1/ ...
=-1/12" is a meaningful statement, even if it shouldn't be interpreted as "the limit of the partial sums" in any sense - it shows that it isn't just a bit of ...
Duration: 7:50
Posted: Jan 9, 2014
Posted: Jan 9, 2014
The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12?
Mar 30, 2022 · By our definitions of limits (and everything else), the sum equals infinity. As you'd expect. Regardless, there are some connections between the ...
Feb 3, 2014 · A recent video purported to prove that adding an infinite series of natural numbers gives you a smaller answer than you might think, ...
Duration: 21:20
Posted: Feb 15, 2024
Posted: Feb 15, 2024
Sep 29, 2022 · It might seem counterintuitive, but the assertion that the sum of natural numbers up to infinity equals -1/12 is based on a particular way of ...
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