Let \(a_0=3\) and \(a_{n}=a_{n-1}+\sqrt{a_{n-1}^2+3}\) for all \(n\ge 1\). Determine \[\lim_{n\to\infty}\frac{a_n}{2^n}.\]

The best solution was submitted by Myeongjae Lee (이명재), 2012학번. Congratulations!

Here is his Solution of Problem 2012-19.

Alternative solutions were submitted by 박민재 (2011학번, +3), 김태호 (수리과학과 2011학번, +3). Two incorrect solutions were submitted (YSC, KJW).