MathDB

Let

n

be a positive integer and let

a_1, \ldots, a_{n-1}

be arbitrary real numbers. Define the sequences

u_0, \ldots, u_n

and

v_0, \ldots, v_n

inductively by

u_0 = u_1 = v_0 = v_1 = 1

, and

u_{k+1} = u_k + a_k u_{k-1}

v_{k+1} = v_k + a_{n-k} v_{k-1}

for

k=1, \ldots, n-1.

Prove that

u_n = v_n.

A1