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. “I learnt this result while lerning string theory…. “ ok. I guess that teaches you more about the validity of string theory than what this video does for maths. Obviously.

  2. First of all you cannot sum a Divergent sequence
    Second: 2*S2 is NOT equal to S1 having finite terms, and its +/- infinity in the case of infinite terms
    Third: The fact that this can be useful in representing some idea doesn't mean its true

  3. When i go to bank to check if my paycheck came, it either came or it didnt, depending on moment in time. I never get half a paycheck. Fking idiots. Youre trying to interpret "either is or isnt" as 1/2 which are the odds of one or another to appear which is different factor

  4. Is actually incorrect, because as he mentioned infinite doesnot give a number, so he is denial, because he thinks s-1/12, is just has nothing to do with infinity.

  5. I was wowed back in high school, but now after calc I know that without checking if the series converges it means nothing.
    If the series was to converge you could say this is the value

  6. No, this simply cannot be true and saying "it's counter-intuitive" just isn't enough to placate any sane mind.
    I don't care how many positive integers you find the sum of, you will NEVER get a negative answer …this is axiomatic.
    We can stop summing anywhere in the sequence and whatever result we have at that point will only get bigger when we continue adding even more positive numbers.

  7. Is s1= 1/2? Or is s1 = 50% probability of being a 1 and a 50% probability of being 0 with an expected value of 1/2? If the latter, then -1/12 doesn’t really work?

  8. Great! Now, can you show me a formula where my $500 bank account should really be $1000000? Once you do that, I will take it to the banker. Thank you!

  9. 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?

  10. 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

  11. 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?

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

  13. 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.

  14. 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.

  15. 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?

  16. 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.


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