Okay, so I have just watched a video explaining to me that the sum
1 + 2 + 3 + 4 + . . . = -1/12
And I want to believe it, though it's mighty counterintuitive.
But I am stuck on something.
The way the proof was presented relied on taking infinite series and adding them together and subtracting them from each other. If we can do that, then why can't I do the following subtraction:
1 + 2 + 3 + 4 + 5 + . . .
-(0 + 1 + 2 + 3 + 4 + . . .)
-------------------------
1 + 1 + 1 + 1 + 1 + . . .
Since the first series is -1/12, and the second series is also -1/12, then the result of the subtraction is 0. In other words:
1 + 1 + 1 + 1 + . . . = 0
Okay, but hold on. If I subtract 1 from both sides, I get:
1 + 1 + 1 + 1 + . . . = -1
So 0 = -1.
And that can't possibly be true.
Where have I gone wrong?
1 + 2 + 3 + 4 + . . . = -1/12
And I want to believe it, though it's mighty counterintuitive.
But I am stuck on something.
The way the proof was presented relied on taking infinite series and adding them together and subtracting them from each other. If we can do that, then why can't I do the following subtraction:
1 + 2 + 3 + 4 + 5 + . . .
-(0 + 1 + 2 + 3 + 4 + . . .)
-------------------------
1 + 1 + 1 + 1 + 1 + . . .
Since the first series is -1/12, and the second series is also -1/12, then the result of the subtraction is 0. In other words:
1 + 1 + 1 + 1 + . . . = 0
Okay, but hold on. If I subtract 1 from both sides, I get:
1 + 1 + 1 + 1 + . . . = -1
So 0 = -1.
And that can't possibly be true.
Where have I gone wrong?
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