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Nov 20, 2009 at 15:24 comment added gowers I think you're right -- and indeed I was worried that something like that would happen. So it seems that the quotients have to grow rather fast to make the number transcendental.
Nov 20, 2009 at 14:21 comment added David E Speyer I don't think this works, see my answer.
Nov 20, 2009 at 11:50 history answered gowers CC BY-SA 2.5