On 30 January 2014 12:45, Jesse Mazer <[email protected]> wrote: > I think the problem is that for non-converging series, there are multiple > similar tricks you could do that would give different answers...for example: > > S = 1-1+1-1+1-1... > -1*S = -1+1-1+1-1+1... > > For a finite or converging series, the order of the summation doesn't > affect the final sum, so if in -1*S we switch the places of the 1st and 2nd > term, similarly with the 3rd and 4th, etc., we get: > > -1*S = 1-1+1-1+1-1... = S > > But if S = -S this implies 2S = 0 which means S=0. > > Another way of getting S=0 would just be to group terms together like this: > > S=1-1+1-1+1-1...=(1-1)+(1-1)+(1-1)+...=0+0+0..., which is a convergent > series with a well-defined sum of 0. > > Likewise, you could also group the terms together like this: > > S = 1-1+1-1+1...=1+(-1+1)+(-1+1)+(-1+1)+...=1+0+0+0..., which again is a > convergent series with a sum of 1. > > Aha! So I was right all along!
I will tell him at some convenient moment... -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
