• services@thehomeworkhelp.co.uk
Call Us Now: 8185279935
Call Us Now: 8185279935
Homework Help
Homework Help
Homework Help
View Details
Homework Help
Assignment Help
Homework Help
Assignment Help
View Details
Assignment Help
Online Tutoring
Online Tutoring
Online Tutoring
View Details
Online Tutoring
Sequence
A sequence is a special case of a function whose domain is the set of all natural numbers N and the range is any set, i.e. a function ƒ : NS is called a sequence. If the range of sequence is any subset of real numbers, then the sequence is called a real sequence.

A real sequence is a function from the set N of natural numbers into the set R of real numbers. In this aspect we shall be dealing with real numbers only, therefore, we shall use the term sequence to denote a real sequence.

A sequence is a rule which associates to each natural number a unique real number.



∀ n ϵ N there exist ƒ(n) ϵ R, where ƒ(n) denotes the real number associated by ƒ to n ϵ N.

The range of the sequence is the set of the values

{ƒ(1), ƒ(2), ….. , ƒ(n), … , } ⊂ R.

Since the domain of all the sequences is the some set N of natural numbers, therefore, a sequence is determined fully if we know

ƒ(n), ∀ n ϵ N.

We shall for the sake of simplicity and clarity, denote ƒ(n) by ƒn and the sequence itself as < ƒn>

∴ < ƒn> = <ƒ1, ƒ2, …. , ƒk, …. , ƒn, …. >


where ƒ1, ƒ2, …., ƒn, … are real numbers and are called first term, second term , …. Nth term of the sequence. The terms ƒ1 and ƒ2 are called distinct terms of the sequence i ≠ j, though ƒi and ƒj are of equal value.

For example, consider the sequence

< ƒn>, where ƒn = (-1)n-1, ∀ n ϵ N

then we find that even terms are of equal values, viz.

ƒ(1) = ƒ(3) = ƒ(5) = …. = 1, 1 ≠ 3 ≠ 5 ≠ ….

and ƒ(2) = ƒ(4) = ƒ(6) = …. = -1, 2 ≠ 4 ≠ 6 ≠ ….

Services: - Sequence Homework | Sequence Homework Help | Sequence Homework Help Services | Live Sequence Homework Help | Sequence Homework Tutors | Online Sequence Homework Help | Sequence Tutors | Online Sequence Tutors | Sequence Homework Services | Sequence



Submit Your Query ???
Topics
Real Number Absolute Value Addition Of Matrices Square Matrix Adjoint Algebraic Structures Alternating Series Linear Equations Determinants Archimedean Real Numbers Binary Operation Binary Relation In A Set Bounded, Unbounded Sets Cauchy Root Test Caylay Hamiltion Theorem Circular Permutation Common Roots Complex Numbers Complex Number Conjugate Conjugate Of A Matrix Constant Sequences Convergence Of A Sequence Cosets Cubic, Biquadratic Equations De Moivre Theorem Real Number Denseness Order 3 Determinants Differences Of Matrices Direct Sum Of Vector Subspaces Eigen Vector Elementary Matrices Matrix Elem. Transformations Equal Matrices Equal Roots Two Permutations Equity Equivalent Matrices Trigonometry Function Expansion Field Function Algebra Fundamental Theorem Gaussian Integer Geometric Series Group Ideals Quantity Increasing Roots Infinite Series Convergent Integers Inverse Of Square Matrix Inverses Of Elementary Matrices Iota, Imaginary Numbers Left-Right Identity Sequence Limit Points Linear Combination Vectors Span Linear Dependence, Independence Linear Homogeneous Equations Two Subspaces Linear Sum Matric Polynomial Matrix Linear Equation Matrix Inverse Matrix Multiplication Matrix Scalar Multiplication Method Of Difference Minors And Co-factors Multiplication Modulo P Normal Sub-Group Normalizer Or Centalizer Orbit Of Permutation Peano Axioms Permutation Function Pigeon Hole Principle Matrices Integral Powers Mathematical Induction Principal Two Determinants Product Two Permutations Product Properties Of Modulus Rank Of A Matrix Rational Numbers Rational, Integral Polynomial Reciprocal Roots Relation Of Sets Rings Of A Set Row By Column Matrix Sequence Series Series Of Positive Terms Series Partial Sum Sequence Subrings Sum Of A Series Cosine Series Sum Sum Of Sine Series Symmetric/Skew Symm. Matrices Roots Symmetric Functions Symmetric Set Degree N Synthetic Division Transformation In General Transformations Of Equations Transpose Of A Matrix Matrix Transposed Conjugate Transposition Complex Numbers Representation Vector Space Vector Sub-spaces Whole Numbers

 

To book a free session write to:- tutoring@thehomeworkhelp.co.uk or call 8185279935