... ,∞n=1an< ∞ and∞n=1(a1a2. . . an)1n> (e − )∞n=1an.1.4. Olympic 1997 161.4 Olympic 19971.4.1 Day 1, 1997Problem 1.Let {n}∞n=1be a sequence of positive real ... ”crosses the axis”infiniteley often.1.5. Olympic 1998 19b) Can a continuous function ”cross the axis” uncountably often?Justify your answer.1.5 Olympic 19981.5.1 Day 1, 1998Problem 1. (20 ... c],1 − x1 − cfor x ∈ [c, 1].1.6. Olympic 1999 21We say that p is an n-periodic point iff(f(. . . f( np))) = pand n is the smallest number with this property. Prove that for everyn...