课程名称︰分析导论优一
课程性质︰数学系大二必修
课程教师︰王振男
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2014/10/14
考试时限（分钟）：40
试题 :
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.