11th Irish 1998 Problem B4 The sequence x 0 , x 1 , x 2 , ... is defined by x 0 = a, x 1 = b, x n+2 = (1+x n+1 )/x n . Find x 1998 .
(1+a+b)/(ab) Solution We calculate x 2 = (1+b)/a, x 3 = (1+a+b)/ab, x 4 = (1+a)/b, x 5 = a, x 6 = b. So x n+5 = x n . Hence x 1998 = x 3 = (1+a+b)/ab. 11th Irish 1998 © John Scholes jscholes@kalva.demon.co.uk 17 Dec 2003 Last updated/corrected 17 Dec 03