Introduction to Sequences and Series

This course deals with series and sequences. It commences with an introduction to sequences and series and then discusses the differences between them. The first section explains how to find the first n terms of a general sequence. The next section introduces arithmetic progression (AP) including the formula for the nth term and the formula for the sum of first n terms. This section explains how to find the nth term and sum of an AP. The next section introduces geometric progression (GP) including the formula for the nth term and the formula for the sum of first n terms. This section explains how to find the nth term and sum of a GP. The course ends with the discussion of the convergent and divergent geometric series.

15 topics

337 lectures

Educators

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Course Curriculum

40 videos

Powers and Polynomial

25 videos

Rational Numbers

11 videos

41 videos

Exponential Functions

15 videos

61 videos

Parametric Equations

5 videos

Introduction to Vectors

15 videos

15 videos

Polar Coordinates

5 videos

30 videos

Introduction to Conic Sections

23 videos

15 videos

Introduction to Combinatorics and Probability

16 videos

Introduction to Sequences and Series

20 videos

Introduction to Sequences and Series Lectures

Introduction to Sequences and Series

General Sequences And Series - Overview

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

Lily An

Introduction to Sequences and Series

General Sequences And Series - Example 1

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

Lily An

Introduction to Sequences and Series

General Sequences And Series - Example 2

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

Lily An

Introduction to Sequences and Series

General Sequences And Series - Example 3

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

Lily An

Introduction to Sequences and Series

General Sequences And Series - Example 4

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

Lily An

Introduction to Sequences and Series

Arithmetic Series - Overview

In mathematics, an arithmetic series is the sum of the terms of an infinite sequence, or the sequence of sums of the terms of such a series. The term arithmetic means that the sequence of numbers is an integer sequence. The sequence can be finite or infinite.

Lily An

Introduction to Sequences and Series

Arithmetic Series - Example 1

In mathematics, an arithmetic series is the sum of the terms of an infinite sequence, or the sequence of sums of the terms of such a series. The term arithmetic means that the sequence of numbers is an integer sequence. The sequence can be finite or infinite.

Lily An

Introduction to Sequences and Series

Arithmetic Series - Example 2

In mathematics, an arithmetic series is the sum of the terms of an infinite sequence, or the sequence of sums of the terms of such a series. The term arithmetic means that the sequence of numbers is an integer sequence. The sequence can be finite or infinite.

Lily An

Introduction to Sequences and Series

Arithmetic Series - Example 3

In mathematics, an arithmetic series is the sum of the terms of an infinite sequence, or the sequence of sums of the terms of such a series. The term arithmetic means that the sequence of numbers is an integer sequence. The sequence can be finite or infinite.

Lily An

Introduction to Sequences and Series

Arithmetic Series - Example 4

In mathematics, an arithmetic series is the sum of the terms of an infinite sequence, or the sequence of sums of the terms of such a series. The term arithmetic means that the sequence of numbers is an integer sequence. The sequence can be finite or infinite.

Lily An

Introduction to Sequences and Series

Geometric Series - Overview

A geometric series is a series of the form a + ar + ar^2 + ... + ar^(n-1). Here r is a non-zero constant and a is a sequence of positive numbers. It is the total of an infinite number of terms. In between successive terms, should have a constant ratio.

Lily An

Introduction to Sequences and Series

Geometric Series - Example 1

A geometric series is a series of the form a + ar + ar^2 + ... + ar^(n-1). Here r is a non-zero constant and a is a sequence of positive numbers. It is the total of an infinite number of terms. In between successive terms, should have a constant ratio.

Lily An

Introduction to Sequences and Series

Geometric Series - Example 2

A geometric series is a series of the form a + ar + ar^2 + ... + ar^(n-1). Here r is a non-zero constant and a is a sequence of positive numbers. It is the total of an infinite number of terms. In between successive terms, should have a constant ratio.

Lily An

Introduction to Sequences and Series

Geometric Series - Example 3

A geometric series is a series of the form a + ar + ar^2 + ... + ar^(n-1). where r is a non-zero constant and a is a sequence of positive numbers. It is the total of an infinite number of terms. In between successive terms, should have a constant ratio.

Lily An

Introduction to Sequences and Series

Geometric Series - Example 4

A geometric series is a series of the form a + ar + ar^2 + ... + ar^(n-1). Here r is a non-zero constant and a is a sequence of positive numbers. It is the total of an infinite number of terms. In between successive terms, should have a constant ratio.

Lily An

Introduction to Sequences and Series

Geometric Convergent vs. Divergent - Overview

In mathematics, a convergent sequence is a sequence of real or complex numbers that has a finite limit, i.e. that has a real or complex value that the sequence tends to as the number of terms increases without bound. The terms of a convergent sequence are said to be "converging" to this limit. A sequence that does not converge is called a divergent sequence. The limit of a convergent sequence is also called its sum. The value of a convergent sequence is also called its sum even when the term "sum" is not otherwise used in the context.

Lily An

Introduction to Sequences and Series

Geometric Convergent vs. Divergent - Example 1

In mathematics, a convergent sequence is a sequence of real or complex numbers that has a finite limit, i.e. that has a real or complex value that the sequence tends to as the number of terms increases without bound. The terms of a convergent sequence are said to be "converging" to this limit. A sequence that does not converge is called a divergent sequence. The limit of a convergent sequence is also called its sum. The value of a convergent sequence is also called its sum even when the term "sum" is not otherwise used in the context.

Lily An

Introduction to Sequences and Series

Geometric Convergent vs. Divergent - Example 2

In mathematics, a convergent sequence is a sequence of real or complex numbers that has a finite limit, i.e. that has a real or complex value that the sequence tends to as the number of terms increases without bound. The terms of a convergent sequence are said to be "converging" to this limit. A sequence that does not converge is called a divergent sequence. The limit of a convergent sequence is also called its sum. The value of a convergent sequence is also called its sum even when the term "sum" is not otherwise used in the context.

Lily An

Introduction to Sequences and Series

Geometric Convergent vs. Divergent - Example 3

In mathematics, a convergent sequence is a sequence of real or complex numbers that has a finite limit, i.e. that has a real or complex value that the sequence tends to as the number of terms increases without bound. The terms of a convergent sequence are said to be "converging" to this limit. A sequence that does not converge is called a divergent sequence. The limit of a convergent sequence is also called its sum. The value of a convergent sequence is also called its sum even when the term "sum" is not otherwise used in the context.

Lily An

Introduction to Sequences and Series

Geometric Convergent vs. Divergent - Example 4

In mathematics, a convergent sequence is a sequence of real or complex numbers that has a finite limit, i.e. that has a real or complex value that the sequence tends to as the number of terms increases without bound. The terms of a convergent sequence are said to be "converging" to this limit. A sequence that does not converge is called a divergent sequence. The limit of a convergent sequence is also called its sum. The value of a convergent sequence is also called its sum even when the term "sum" is not otherwise used in the context.

Lily An