Of course Thanks!
I don't think induction is necessary. To show that this is always positive, show that the numerator and denominator are always the same sign (I can't see any reason why either of them would ever be negative...)
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??The denominator is just . Saying that "I can't see any reason why either of them would ever be negative" is exactly the same as saying "I can't see any reason why wouldn't be positive"- and that does NOT constitute a proof that it is!
Indeed, since the numerator, is obviously always positive, saying "show that the numerator and denominator are always the same sign" is exactly the same as saying "show that is always positive" which is exactly what the original problem says!