CK-12-Pre-Calculus Concepts

11.4. De Moivre’s Theorem and nth Roots http://www.ck12.org Guided Practice Check the three cube roots of 8 to make sure they a ...

http://www.ck12.org Chapter 11. Complex Numbers (√ 2 − √ 2 i ) 6 = (2 cis 315◦)^6 = 26 ·cis( 6 · 315 ◦) = 64 ·cis( 1890 ◦) = 64 ...

11.5. References http://www.ck12.org 11.5 References CK-12 Foundation.. CCSA CK-12 Foundation.. CCSA CK-12 Foundation.. CCSA CK ...

http://www.ck12.org Chapter 12. Discrete Math CHAPTER 12 Discrete Math Chapter Outline 12.1 Recursion 12.2 ARITHMETIC ANDGEOMETR ...

12.1. Recursion http://www.ck12.org 12.1 Recursion Here you will define patterns recursively and use recursion to solve problems ...

http://www.ck12.org Chapter 12. Discrete Math Solution: 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 = 143 Example B Write a re ...

12.1. Recursion http://www.ck12.org You can choose any starting positive integer you like. Here are the sequences that start wi ...

http://www.ck12.org Chapter 12. Discrete Math 12.2 Arithmetic and Geometric Sequences Here you will identify different types of ...

12.2. Arithmetic and Geometric Sequences http://www.ck12.org a 1 =a 1 a 2 =a 1 +d a 3 =a 1 + 2 d a 4 =a 1 + 3 d ... an=a 1 +(n− ...

http://www.ck12.org Chapter 12. Discrete Math Example C For the following sequence, determine the common ratio or difference and ...

12.2. Arithmetic and Geometric Sequences http://www.ck12.org different way. − 3 , 2 , 7 , 12 , 17 ,... You should see the common ...

http://www.ck12.org Chapter 12. Discrete Math 12.3 Sigma Notation Here you will learn how to represent the sum of sequences of n ...

12.3. Sigma Notation http://www.ck12.org Example B Write the sum in sigma notation: 2+ 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 Solution: ...

http://www.ck12.org Chapter 12. Discrete Math Just like summation uses a capital Greek letter forS, product uses a capital Gree ...

12.4. Arithmetic Series http://www.ck12.org 12.4 Arithmetic Series Here you will learn to compute finite arithmetic series more ...

http://www.ck12.org Chapter 12. Discrete Math 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 3 + 7 + 11 + 15 + 19 = 10 + 26 + 19 = 36 ...

12.4. Arithmetic Series http://www.ck12.org Evaluate the following sum. 500 i∑= 02 i−^312 Answers: The initial term is -1 and t ...

http://www.ck12.org Chapter 12. Discrete Math 100 i∑= 0 i−^15 85 i∑= 0 −^13 i+^1 212 i∑= 0 −^2 i+^6 12.^54 ∑ i= 0 6 ...

12.5. Geometric Series http://www.ck12.org 12.5 Geometric Series Here you will sum infinite and finite geometric series and cate ...

http://www.ck12.org Chapter 12. Discrete Math The left side of this equation is a geometric series with starting term 1 and comm ...