### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Sequence

A real sequence is a function whose domain is the set of positive integers and range is a subset of the set of real numbers, i.e.,

Example:

Let , then is a sequence in .

Limit of Sequence:

Definition:

We say that a sequence of real numbers converges to a real number   if for every there is an such that i.e., a sequence converges at all it has to converge to a unique real number which we call its limit, we express this by

where the symbol stands for approaches or tends to.

Properties:

If and then,

Where

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