課程名稱︰分析導論優一
課程性質︰數學系大二必修
課程教師︰王振男
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/10/14
考試時限（分鐘）：40
試題 :
3
1. (10%) A real sequence {x } satisfies 7 x = x + 6 for n ≧ 1. If x = 1/2,
n n+1 n 1
prove that the sequence increases and find its limit. What happens if x =
1
3/2 or if x = 5/2 ?
1
2. (5%) (a) The intersection of an arbitrary collection of compact subsets of M
is compact.
(5%) (b) The union of a finite number of compact subsets of M is compact.