← JEE Class JEE
Sequences and Series
Chapter Overview
AP: nth term, sum, arithmetic mean. GP: nth term, sum, geometric mean, sum to infinity. Harmonic progression (HP). Arithmetic-Geometric progression (AGP). Special series: sum of naturals, squares, cubes. Method of differences, telescoping sums. Inequalities involving AM, GM, HM (AM >= GM >= HM).
Topics Covered
- Arithmetic Progression
- Geometric Progression
- Harmonic Progression
- AGP
- Special Series
- Method of Differences
- Telescoping
- AM-GM-HM Inequality
Key Formulas
AM = (a+b)/2
GM = √ab
HM = 2ab/(a+b)
AM >= GM >= HM
sum k = n(n+1)/2
sum k2 = n(n+1)(2n+1)/6
Real-World Applications
Applications: JEE problem solving, growth models, financial mathematics.
Study Tips
Tip: Learn all summation formulas
Tip: Practice AM-GM inequality problems
Tip: Master telescoping sums