OK... thanks, I should have guesses it was the zeta function :D Anyway, I showed this proof to my 15 year old son and he soon put me right on why 1-1+1-1+1-1+1... is indeed 1/2.
call the series 1-1+1-1+1... S then 1-S = 1 - (1-1+1-1+1-1+1...) = 1-1+1-1+1-1... = S S=1-S, so S=1/2 (which is, I should think, another way of writing Bruno's proof, above, but maybe even simpler!) Actually that *does *look rigorous. I mean, assuming that infinite series exist and can be added up, etc, etc, that answer looks fairly watertight. What could possibly go wrong? -- 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.
