# Thread: The Sum of All Natural Numbers = -1/12

1. ## The Sum of All Natural Numbers = -1/12

2. I know the mathematician on the left looks hideous. But if anybody's watched the video, do you have an explanation for the move from step 1 to step 2?

3. Essentially, you can do anything to an equation as long as you'd keep it balanced. You can 'prove' your own assumption(s) or use one(s) that has been proven. The aim is to continually get the numbers into a condensed enough form to properly solve. In S2: Adding the equation to itself has been shown as valid as well as the process of shifting it... since you are not changing any of the values. Any mathematical proof is valid unless a part of it can be disproved.

4. Originally Posted by LittleV
Essentially, you can do anything to an equation as long as you'd keep it balanced. You can 'prove' your own assumption(s) or use one(s) that has been proven. The aim is to continually get the numbers into a condensed enough form to properly solve. In S2: Adding the equation to itself has been shown as valid as well as the process of shifting it... since you are not changing any of the values. Any mathematical proof is valid unless a part of it can be disproved.
You say that shifting the lower series when adding them is "as valid as" balancing an equation. That's true because nothing has been added to the second series, it's just a null value at the beginning of the series. Adding nothing to a series doesn't change the series.

There is more to the proof, it has to do with convergent and divergent series. The idea is to cause the sum of the two series to converge, but the theory behind this is not included in the video.

5. Originally Posted by Mal12345
You say that shifting the lower series when adding them is "as valid as" balancing an equation. That's true because nothing has been added to the second series, it's just a null value at the beginning of the series. Adding nothing to a series doesn't change the series.

There is more to the proof, it has to do with convergent and divergent series. The idea is to cause the sum of the two series to converge, but the theory behind this is not included in the video.
I wouldn't compare the two; some notions are more likely to be disproved than others... balancing is not one that is in question. Yes... adding the series to itself and multiplying the 'S2' by two is keeping it balanced. When you'd shift the second row to add the numbers... this is a rule that many are taken aback by initially (so I thought I'd mention that). It's deemed as valid in itself because none of the individual values would be changed in doing so -- the top and bottom would always equal one another. There is more than just 'balancing' involved here... but it seems solid so far.

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