. , ∞ n=1 a n < ∞ and ∞ n=1 (a 1 a 2 . . . a n ) 1 n > (e − ) ∞ n=1 a n . 1.4. Olympic 1997 16 1.4 Olympic 1997 1.4.1 Day 1, 1997 Problem 1. Let { n } ∞ n=1 be a sequence of positive real. ”crosses the axis” infiniteley often. 1.5. Olympic 1998 19 b) Can a continuous function ”cross the axis” uncountably often? Justify your answer. 1.5 Olympic 1998 1.5.1 Day 1, 1998 Problem 1. (20. . . . . . . . . . . . . . 9 1.2.2 Day 2, 1995 . . . . . . . . . . . . . . . . . . . . . 10 1.3 Olympic 1996 . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.1 Day 1, 1996 . . . . . . .