Chapter 6: Sequences and Series

6.1: Introduction

1. Introduction to Sequence and Series
2. Problem-Introduction to Sequence and Series
3. Convergent, Divergent and Periodic Sequences
4. Problem-Convergent, Divergent and Periodic Sequences

6.2: Types of Sequences

1. Types of Sequences
2. Problem-Types of Sequences

6.3: Arithmetic Progression (A.P)

1. Concept of Arithmetic Progression
2. Problem-Concept of Arithmetic Progression

6.4: Arithmetic Mean (A.M)

1. Concept of Arithmetic Mean
2. Problem-Concept of Arithmetic Mean
3. n Arithmetic Means Between Two Given Numbers

6.5: Series

1. Concept of Series
2. Problem1-Concept of Series
3. Problem2-Concept of Series
4. Sum of First n Terms of an Arithmetic Series
5. Problem-Sum of First n Terms of an Arithmetic Series
6. To Find the Sum of n A.M
7. Problem-To Find the Sum of n A.M
8. To Find the Sum of p A.M
9. Problem-To Find the Sum of p A.M

6.6: Word Problems on A.P

1. Word Problems on Arithmetic Progression
2. More on Word Problems on Arithmetic Progression
3. Problem1-Word Problems on Arithmetic Progression
4. Problem2-Word Problems on Arithmetic Progression

6.7: Geometric Progressions (G.P)

1. Concept of Geometric Progression
2. Problem1-Concept of Geometric Progressions
3. Problem2-Concept of Geometric Progressions

6.8: Geometric Means

1. Concept of Geometric Mean
2. Problem-Concept of Geometric Means
3. n Geometric Means Between Two Given Numbers
4. Problem-n Geometric Means Between Two Given Numbers

6.9: Sum of n Terms of a Geomeric Series

1. Introduction to Geometric Series
2. Problem-Introduction to Geometric Series
3. Sum of n Terms of a Geometric Series
4. Problem-Sum of n Terms of a Geometric Series

6.10: The Infinite Geometric Series

1. The Infinite Geometric Series
2. More on The Infinite Geometric Series
3. Problem1-The Infinite Geometric Series
4. Problem2-The Infinite Geometric Series
5. Recurring Decimals

6.11: Word Problems on G.P

1. Word Problems on Geometric Series
2. More on Word Problems on Geometric Series
3. Problem1-Word Problems on Geometric Series
4. Problem2-Word Problems on Geometric Series
5. Problem3-Word Problems on Geometric Series

6.12: Harmonic Progerssion ( H.P)

1. Concept of Harmonic Progression
2. Problem-Concept of Harmonic Progression
3. General Term of Harmonic Progression
4. The Characteristic Relation for H.P
5. Problem-The Characteristic Relation for H.P
6. An Important Theorem
7. More on An Important Theorem
8. Problem-An Important Theorem
9. Problem-General Term of Harmonic Progression
10. Concept of Harmonic Mean
11. Problem-Concept of Harmonic Mean
12. n Harmonic Means Between Two Numbers
13. Problem-n Harmonic Means Between Two Numbers

6.13: Relations Between Arithmetic, Geometric and Hamonic Means

1. Relations Between A.M, G.M & H.M
2. More on Relations Between A.M, G.M & H.M
3. Problem-Relations Between A.M, G.M & H.M

6.14: Sigma Notation ( or Summation Notation )

1. Sigma Notation ( or Summation Notation )
2. Problem 1-Sigma Notation ( or Summation Notation )
3. Problem 2 -Sigma Notation ( or Summation Notation )

6.15: To Find Formulae For The Sums

1. Sum of Positive Integral Powers of Natural Numbers
2. Alternate Formula For sum of n Numbers
3. Problem-Alternate Formula For sum of n Numbers
4. Alternate Formula For Sum of n Squares
5. More on Alternate Formula For Sum of n Squares
6. Problem-Alternate Formula For Sum of n Squares
7. Alternate Formula For Sum of n Cubes
8. More on Alternate Formula For Sum of n Cubes
9. Problem1-Alternate Formula For Sum of n Cubes
10. Problem2-Alternate Formula For Sum of n Cubes
11. Arithmetical-Geometric Series
12. Problem-Arithmetical-Geometric Series
13. Sum of n Terms of Arithmetical-Geometric Series
14. More on Sum of n Terms of Arithmetical-Geometric Series
15. Further on Sum of n Terms of Arithmetical-Geometric Series
16. Problem-Sum of n Terms of Arithmetical-Geometric Series
17. Sum to Infinity of Arithmetico-Geometric Series
18. Problem-Sum to Infinity of Arithmetico-Geometric Series
19. The Method of Differences
20. Problem-The Method of Differences
21. A Series Each Term Having r Factors in A.P
22. More on A Series Each Term Having r Factors in A.P-1
23. More on A Series Each Term Having r Factors in A.P-2
24. More on A Series Each Term Having r Factors in A.P-3
25. Problem-A Series Each Term Having r Factors in A.P
26. Introduction to Reciprocal Series
27. More on Introduction to Reciprocal Series1
28. More on Introduction to Reciprocal Series2
29. More on Introduction to Reciprocal Series3
30. Problem-Introduction to Reciprocal Series1
31. Problem-Introduction to Reciprocal Series2
32. Summation of Series By Partial Fractions
33. Problem-Summation of Series By Partial Fractions