## Sequences and Series

# Basic Concepts

- Sequence is an arrangement of numbers in definite order according to some rule
- A sequence is a function whose domain is a set of natural numbers. If the range of a sequence is a subset of real numbers (complex numbers), then it is called a real sequence (complex sequence)
- Finite sequences : A sequence is said to be finite if it has finite number of terms.
- Infinite sequences : A sequence is said to be infinite if it has infinite number of terms.
- If a
_{1}, a_{2}, a_{3}- - - a_{n}is a sequence, then the expression a_{1}+ a_{2}+ a_{3}+ - - - - - + a_{n}is a series. - Sequences following specific patterns are called progressions.

### Part1: View the Topic in this video From 00:40 To 53:02

### part2: View the Topic in this video From 00:40 To 55:31

### Part3: View the Topic in this video From 00:40 To 50:21

### Part4: View the Topic in this video From 00:40 To 37:04

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- The finite series x
_{1}+ x_{2}+ x_{3}+..... +x_{n}=\sum_{k=1}^{n} \ x_{k} - The infinite series x
_{1}+ x_{2}+ x_{3}+..... +x_{n}+...... ∞ = \sum_{i=1}^\infty \ x_{i}