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1+2+3+4+...=-1/12? proof

by fargoth
Tags: 1 or 12, proof
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Feb20-14, 02:32 AM
P: 400
I've see this neat proof: (for some reason the youtube tag didn't work in preview...)
And now I don't see how what I've learned about series convergence is true...
I've been told that if [itex]a_n > b_n \forall n[/itex] then [itex] \sum a_n > \sum b_n [/itex] therefore, if [itex] \sum b_n [/itex] is divergent then, [itex] \sum a_n [/itex] must be too.
Also, If the partial sum diverges, the series is said to be divergent, isn't it?
And what about [itex] a_n \neq 0 [/itex] for n that tends to infinity?
So many ways I could show this series diverges, yet he show it's equal to -1/12???

Where am I, or is he, wrong?
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Feb20-14, 02:57 AM
P: 18
I think this cannot be true. The sum of all natural numbers up to N equals (as also shown in the end of the video) ## N(N+1)/2 ##. This obviously goes to infinity as N goes to infinity. And of course there is also no way how strictly positive numbers can add up to give a negative result.
Feb20-14, 03:01 AM
P: 400
That's what I was saying :)
So where is he wrong?

Feb20-14, 03:13 AM
P: 542
1+2+3+4+...=-1/12? proof

A recent thread on this...
Feb20-14, 03:28 AM
Borek's Avatar
P: 23,536
And as this link was posted we can safely close the thread.

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