# Generalization is my frenemy

Consider the generalization of the Fibonacci sequence: define the $$n$$-bonacci sequence such that its term is sum of the previous $$n$$ terms with initial terms: $$a_{0,n} = a_{1,n} = a_{2,n} = \ldots = a_{n-2,n} = 0, a_{n-1,n} = 1$$.

Now we denote the $$m^\text{th}$$ term of the $$n$$-bonacci sequence as $$W_{m,n}$$. Calculate the limit below.

$\large \lim_{n \to \infty} \lim_{m \to \infty} \frac { W_{m+1,n} }{W_{m,n}}$

Details and Assumptions:

• As an explicit example: if $$n=2$$, we will get a Fibonacci sequence, which means the limit is $$\phi = \frac { 1 + \sqrt 5}{2}$$.

• You do not need computational aids to solve this problem.

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