Ooooh. Very close. Unless I’m wrong, [Sym]S/Sym converges to -ln(1-x) for -1 [Sym]£[/Sym] x < 1.
Yup; I suppose I should have explicitly indicated that the minus sign is part of the power series too (I DID have that shown in my first post, at least). But of course that doesn’t change the radius of convergence.
quote:
Originally posted by ultrafilter
Just bear in mind that that’s not a proof, though, as it starts from the assumption that both sides are equal.
However, if all the steps are reversible (as they are in this case), you can turn it into a real proof by reading it backwards. Start with the known true identity at the end, then do each step in reverse to arrive at the desired result.
However, if this was supposed to be an exercise in mathematical induction, then you haven’t proved it in the way that was supposed to be used.
I realize that that’s not a proof as written. I only included what was needed to make the GQ answerable. I have the rest of the proof written down at home, for my assignment.
Good. A lot of people don’t realize that, though, so I was just making sure.