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

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EXTRA ARTICLE BY TONY:
The sum of all natural numbers (from 1 to infinity) produces an “astounding” result.
ANOTHER PROOF & EXTRA FOOTAGE:
MORE:
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….

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. You cannot assume that Σ(-1)^n is 1/2, that is a divergent series right? You cannot average the nth value.

4. Doesn't shifting the S2 series no longer make it 2(S2)?

5. Interesting how Infinity, which yeah we can't really explain, is equal to -1/12

6. Διονυσης Αρβανιτακης

Physicists who know that little about mathematics are dangerous

7. 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

8. Why we push this number

9. WARROBOTS GAMER JUGADORROBOTS EN GUERRA

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.

10. 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

11. 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.

12. 1+2+3+4+5+6+7+8+9+10+11+12… = infinity.

13. 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?

14. If these professors really believe this and physics uses this we're in very serious trouble and so is Numberphile.

15. 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!

16. 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?

17. Wasted 8 minutes of my life

18. This the Ramanujan series

19. 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

20. 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?

21. He changed the problem so therefore it’s not true

22. This video explains in 7:49 minutes why modern physics is a scam. (esp. String Theory)

23. I love how happy he is with this haha

24. It's all about Indian mathematician ramanujan u fkin mathematician

25. It’s time this Ramanujan mistake was finally put to bed.

26. Don't forget the founder of this ..

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

28. Hey you sucker this is Ramanujan infinity equation not your..

29. 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.

30. 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.

31. Oof. This is embarrassing. Physicists who can’t do maths.

Why haven’t you taken this down?

32. and this is why one does not simply count to infinity

33. I feel like I need to go rock in a corner muttering to myself.

34. 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?

35. If 1+2+3+4+5…=-1/12

Add 1/12 to both sides of equation

∞ = 0
Lol

36. Can any physicist confirm here that this result is useful in quantum theory despite it being mathematically incorrect?

37. Two minutes silence for those fools for whom this trolled invention is crazy video….🤣🤣🤣

38. I just don't get if bill gates doesn't stop earning money he'll become poor!?

39. 1+2+3+4+5….=infinity
That's truth

40. Before i watched this video: i think thats wrong.

After i watched this video: bunch of imbeciles.

41. And this, children, is how Common Core began…

42. I thought this was an april fools joke
then I checked the date and went into denial
Got I wonder how this works

43. By Ramanujan

44. "The answer can be either 1 or 0, so we take the average 1/2." WHAT?????? WHY???? HOW????

45. if (infinity) = (intifinity) + (all of numbers), than it's true.

46. 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.