But I’m sure, as I will think about it more, read more proofs and work with it, I’ll come to regard it as obviously right. But will it be any more obvious than before?
If you’re interested, here is a good explanation of the derivation of the formula. I don’t think it’s obvious, any more than the quadratic formula is obvious: it’s just one of those mathematical tricks that you learn and becomes second nature.
I’m not sure I’m completely happy with that explanation. They use the result that ln(1+x) is very close to x when x is small. This is due to the Taylor series expansion of ln(1+x) (edit:or simply on looking at the ratio of the two and using L’Hospital’s rule), but if one hasn’t had calculus, that claim is going to look like magic.
If you’re interested, here is a good explanation of the derivation of the formula. I don’t think it’s obvious, any more than the quadratic formula is obvious: it’s just one of those mathematical tricks that you learn and becomes second nature.
I’m not sure I’m completely happy with that explanation. They use the result that ln(1+x) is very close to x when x is small. This is due to the Taylor series expansion of ln(1+x) (edit:or simply on looking at the ratio of the two and using L’Hospital’s rule), but if one hasn’t had calculus, that claim is going to look like magic.