Question 155
Let $f: \mathbb{N} \rightarrow [0, \infty)$ be a function satisfying the following conditions:
a) $f(4) = 2$;
b) $\frac{1}{f(0) + f(1)} + \frac{1}{f(1) + f(2)} + \ldots + \frac{1}{f(n) + f(n+1)} = f(n+1)$, for all integers $n \geq 0$.
Find $f(n)$ in closed form.
a) $f(4) = 2$;
b) $\frac{1}{f(0) + f(1)} + \frac{1}{f(1) + f(2)} + \ldots + \frac{1}{f(n) + f(n+1)} = f(n+1)$, for all integers $n \geq 0$.
Find $f(n)$ in closed form.