5.) Given: Carlos is tall. Paul is short. Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 5.) Given: Carlos is tall. Paul is short. a.) Jenny is shorter than Paul. What do we know about Jenny? b.) Dave is taller than Carlos. What do we know about Dave? c.) Beth is taller than Paul. What do we know about Beth? d.) Sofia is shorter than Carlos. What do we know about Sofia? e.) Carlos has a younger brother Manuel who is 12. Manuel has been the same height that Carlos was as he has grown up. Will Manuel be tall? Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Keep it in the family (emogis) Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Keep it in the family (emogis) Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Keep it in the family Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Keep it in the family Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.4 Direct and Limit Comparison Tests 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Practice:  Pg. 587 #3, 5, 8, 15-22, 29-36, 45, 46 Monday, December 31, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals