Quant Interview Question

Question

How do you impress the interviewer, when he asks you to compute $\sqrt{2+\sqrt{2+\sqrt{2+...}}}$?

To impress you would start by properly defining it as the limit of a recurrence, then show that this recurrence converges (showing that the expression is well-defined) and then in the end you find the limit. — Winther, Apr 02 '17 at 18:15
By saying the limit is trivially $2$ by the Banach fixed point theorem. — Jack D'Aurizio, Apr 02 '17 at 21:18

score 3 · Answer 1 · answered Apr 02 '17 at 18:13

3

Just note that $$x^2-2=x$$ I bet even a quant can solve that. (I'm allowed to make that joke, I'm actually a quant myself.)

answered Apr 02 '17 at 18:13

Matt Samuel

score 0 · Answer 2 · answered Apr 02 '17 at 18:22

0

If $x=\sqrt{2+\sqrt{2+\sqrt{\dots}}}$, then $x=\sqrt{2+x}$ so that $x^2-x-2=0$. Thus $x=\frac{1+\sqrt{1+4(2)}}{2}=2$.

answered Apr 02 '17 at 18:22

Shaun

2 Answers2