(Solved): Problem 3. Let (Up, U1, U2, U3, ......) Be A Sequence Of Real Numbers. We Write This As (Un)neN. We ...

Problem 3. Let (Up, U1, U2, U3, ......) be a sequence of real numbers. We write this as (Un)neN. We say that it is: • bounded above when: 3 AER such that (Un E N, un < A). • bounded below when: 3 BER such that (Vn e N, Un > B). We say that it converges towards too when: VA > 0, 3 m EN such that VnEN, (n > m = Un > A). 1. Write in quantifiers the statement: (Un)nen is not bounded below. 2. Give an example of sequence of real numbers (un)neN which is bounded above but not bounded below. 3. Write in quantifiers the statement: (un)nen does not converge towards too. Page 1 Due in week 5 Mathematics 220, Spring 2020 Homework 4 Due in week 5 4. Show that the sequence of real numbers defined by Un = (-2)" VEN does not converge towards too.