User:Sjelin

The base case is trivial, so I'll skip to the inductive step

To see why combining limits is totally not allowed, consider the following limit: $$\lim_{x\rightarrow 0} \lim_{y\rightarrow 0} \frac{x+y}{x+2y} = \lim_{x\rightarrow 0} \frac{x}{x} = 1 \neq \lim_{x\rightarrow 0} \frac{x+x}{x+2x} = 2/3$$

Of course, this does not disprove your formula, in fact I think your formula is probably right in most cases, if not all cases. I simply can't see how to prove your formula.