MathDB
2013 BMT Individual 17

Source:

January 18, 2022
algebra

Problem Statement

Let N≥1N \ge 1 be a positive integer and kk be an integer such that 1≤k≤N1 \le k \le N. Define the recurrence xn=xn−1+xn−2+...+xn−NNx_n = \frac{x_{n-1} + x_{n-2} +... + x_{n-N}}{N} for n>Nn > N and xk=1x_k = 1, x1=x2=...=xk−1=xk+1=..=xN=0x_1 = x_2 = ... = x_{k-1} =x_{k+1} =.. = x_N = 0. As nn approaches infinity, xnx_n approaches some value. What is this value?
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