Let M>0 be a real number. Prove that there exists N so that if n>N, then all the roots of \(f_n(z)=1+\frac{1}{z}+\frac1{{2!}z^2}+\cdots+\frac{1}{n!z^n}\) are in the disk |z|<M on the complex plane.

The best solution was submitted by Jeong, Seong Gu (정성구), 수리과학과 2007학번. Congratulations!

Here is his Solution of Problem 2010-9.

Alternative solutions were submitted by 최홍석(화학과 2006학번, +3), 김호진(2009학번, +3), 김치헌 (수리과학과 2006학번, +3).