Register to reply

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

by fargoth
Tags: 1 or 12, proof
Share this thread:
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?
Phys.Org News Partner Mathematics news on
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
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: 533
1+2+3+4+...=-1/12? proof

A recent thread on this...
Feb20-14, 03:28 AM
Borek's Avatar
P: 23,386
And as this link was posted we can safely close the thread.

Register to reply