Exercises

• Course: Math 280(Introduction to real analysis)

Section2-1:1---5,7,8,10,11,12,16
Section2-2:1,2,4,6,12(all except c),14,15
Section2-3:1,2,3,4,5,8
Section 2.4 :1,2,3,4,5,6,8
Section 3.1:1,2(a,b,),4,5,6
Section 3.2:1,2,3,4,14,15
Section 3.4: 8
Section 3.5: 1,2,3
More exercises for  section 3.5:
(a) Show that if (xn) is Cauchy then ((xn)2) is also Cauchy.

(b) Give an example of a Cauchy sequence ((xn)2) such that (xn) is not Cauchy
Explain why the sequence defined by an = (  -1)n is not a Cauchy sequence

Show that every subsequence of a Cauchy sequence is itself a Cauchy sequence.

Section 5-1:1,2,3,4,5
Section 5.2 :1,2,3,4,5,6

Section 6-1:2,3,5,6,7,8,9,13,14,16
section6-2:1,2 ,3,4
section 6-3:2,8,12
section 7-1: 1,2,4,5,6,8