/sci/ - Science & Math

>>11559084
Suppose the sequence converges to [math]a[/math]. By recursivity, we have [math]a = 1 + \frac{1}{a} \Leftrightarrow a^2 = a + 1 \Leftrightarrow a^2 - a - 1 = 0[/math]. This gives us [math] a = \frac{1 \pm \sqrt{5}}{2}[/math], and the necessary positivity of [math]a[/math] eliminates the other option.