The study guide for Class 11 Sequences and Series covers the definition and notation of sequences, as well as various types of sequences and their formulas.

Sequences

• A sequence is an ordered list of objects or numbers, denoted by "term" and is described as a pattern in words or a relationship between terms.
• It can be described mathematically through explicit mathematical functions and recursive formulas.
• The domain and range of a sequence, whether finite or infinite, are important notations to consider.
• Notations such as "a" or "t" are often used to represent a term, with "an" denoting the "n-th" term in the sequence.
• Arithmetic and geometric sequences involve specific formulas and properties to calculate the terms and the sums of the sequence.

Series

• The series is the sum of the terms in a sequence and can be calculated using various notations and properties, such as the summation notation and general summation properties.
• Special series formulas and properties are given for specific types of series.
• Partial sum formulas for arithmetic and geometric series are provided, along with key considerations for convergence and divergence.

Exponential Functions and the Number e

• Exponential functions, their formulas, and properties are discussed in the context of dependent and independent variables, as well as growth and decay.
• The natural number "e" is introduced as the base for exponential functions, with applications in continuous compounding and various real-world scenarios.

Logarithmic Functions and Properties

• Logarithmic functions are introduced as the inverses of exponential functions and are used for solving exponential equations.
• Special logarithmic values and properties are discussed, including common logarithms and the natural logarithm.

By understanding the concepts and formulas related to sequences, series, exponential, and logarithmic functions, students can build a strong foundation in calculus and mathematical analysis. This study guide provides a comprehensive overview of these topics with examples, properties, and applications.

For more in-depth learning, students can access additional resources such as Sequences and Series worksheets, questions and answers PDFs, Khan Academy tutorials, and calculus books that cover sequences, series, exponential and logarithmic functions in further detail.