MathDB

2017 BMT Individual 18

Source:

January 9, 2022

algebra

Problem Statement

Consider the sequence

(k_n)

defined by

k_{n+1} = n(k_n + k_{n-1})

and

k_0 = 0

k_1 = 1

. What is

\lim _{n\to \infty} \frac{k_n}{n!}