ASTOUNDING: 1 + 2 + 3 + 4 + 5 + … = -1/12


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The sum of all natural numbers (from 1 to infinity) produces an “astounding” result.
NY Times article on this:

Tony Padilla and Ed Copeland are physicists at the University of Nottingham.

They talk physics at our sixty symbols channel:

Grandi’s Series: 1-1+1-1….

Read more about divergent series:
We also here that Chapter XIII of Konrad Knopp’s book, “Theory and Application of Infinite Sequences and Series”, is very good if you can get your hands on it.

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  1. Uncorrected, this video has misled millions. Charisma does not sum up to truth. Where is the follow-up correction? How many more will watch, believe and befuddle all their various fields?

  2. Its actually not true, it’s wrong because you are assuming the first sum equals to 1/2, which is false, it’s either 1 or 0, you only get this if you get that 1/2 just because now you want to change how math works, at least in this explanation the answer is wrong, maybe they have proven it in a real complex way for us mortals to understand it, but this ain’t it, for me that’s still infinite

  3. 1 is a positive integer.
    Each of the rest of the numbers in the sequence to be added is also a positive integer.
    If you add a positive integer to a positive integer, you get another positive integer. (…or you need to use a larger word size.)
    Therefore, if sum(1..n) is a positive integer, so is sum(1..n+1).

    Therefore, sum(1…+inf), IF IT EXISTS, must be a positive integer.

    How can you claim that an oscillating sequence, or a diverging one, has any kind of meaningful sum at all?

  4. This is a faulty proof which shoes what happens when you treat infinity as a number.
    In reality,
    S – S2 = Infinity – 1/4 = Infinity

  5. 1 – 1 + 1 – 1 + 1 – 1 ± … = 1/2

    The proof that the sum of Grandi series above is equal to 1/2 is very simple.
    What you have to do is simply to evaluate its ordinary generating function 1/(1+x) at x=1. That's all.

  6. Anyone who can come up with an answer to the sum of the divergent series of repeating units below
    1 + 11 + 111 + 1111 + 11111 + 111111 + … = ?

    Hint: You need to start from a geometric series.

  7. So what's the sum of all positive even integers (2 + 4 + 6 + 8 + 10 + …)? Would it be -1/24 because we've removed half the numbers in the series of all positive integers? Or would it be -1/6 because we've doubled every number in that series?

  8. The sum of the infinite series of 1-1+1-1+1-1… Isn't 1/2, in fact it's not anything. Unless the infinite series diverges towards something (positive or negative infinity, or some finite number) it has no result. The sum of all natural numbers is infinitity, or Aleph Null.

  9. I never will not believe that it is true.
    It's like saying that numbers are not in a straight line but they are in a parabola

  10. If 1 + 2 + 3 + 4 + … = -1/12 then I bet we live in a simulation, and the computers reckoning that sum crash everytime they are fed this series.


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