HOME COURSES PREVIEW REVIEW ABOUT CONTACT
Toll-Free Info & Ordering
M-F: 9am-5pm (PST):
(877) RAPID-10
24/7 Technical Support
QUICK TOUR
Member Login:
Rapid Learning Member Login

Rapid Courses Catalog
Math Survival Weekly
Get the insider's tips and tricks in how to survive your math course and ace the next test. Subscribe the Web's only math weekly newsletter for students and learn:
- How to Study Math Effectively
- How to Take Math Courses Strategically
- How to Solve Math Problems Systematically
- How to Score High in Math Exams
- How to Master Math Rapidly

Enter your name and email below and get started today!
Your Name * 
Email * 
 
Math Study Lounge
These study sheets are for quick review on the subjects. Refer to our rapid courses for comprehensive review.
    - Getting Started with Algebra
    - Geometry Basics
    - How to Solve Math Problems
    - Trigonometry Quick Review
    - Statistics At-A-Glance
    - Calculus Preview

Sequences and Series

Topic Review on "Title":

The definition of infinite sequences: 
An (infinite) sequence of real numbers is a function from the positive integers n into real numbers ,

Limit of a sequence:
A sequence of real numbers converges to the number  if, for any  there is a positive integer such that for any  is called the limit of the sequence .

Convergence of Cauchy sequences:

A sequence of real numbers converges if and only if it is a Cauchy sequence.

Subsequences of a sequence:
Subsequences are formed when we have a strictly increasing sequence of positive integers.

Convergence tests:
The comparison test, ratio test, root test, integral test and absolute/ conditional convergence test are the tests that are used to determine the convergence of series.


Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

This tutorial specifically describes the concepts of infinite sequences and series. Examples are presented to with the basic operations and properties of infinite sequences. Applying some type of theorem to find the limit is important when dealing with sequences.  

The properties of sequences with applications to approximation of limits are shown in the examples. The uniqueness and convergence of sequences need to be discussed before the concept of subsequences is defined. Sequences need to be bounded and monotonic so they can be classified as convergent sequences. Special sequences such as Cauchy sequences are also mentioned in this tutorial.


Tutorial Features:

Specific Tutorial Features:
• Graphs showing the convergence of sequences.
• Step by step analysis of the different types of convergence tests that can be used to determine is a series converges or not.

Series Features:
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.


"Title" Topic List:
Infinite sequences
Arithmetic and geometric progression
Definition of sequences
Recursive relations
Limit of a sequence
Divergence of sequences
Operations of a limit
Bounded and monotonic sequences
Definition of Cauchy sequences
Convergence of Cauchy sequences
Subsequences
Infinite series
Arithmetic sum
Geometric Series
Basic properties of series
Comparison test
Ratio, root, integral, p-series and alternating series test

See all 24 lessons in College Algebra, including concept tutorials, problem drills and cheat sheets: Teach Yourself College Algebra Visually in 24 Hours

Home  |   Courses  | Preview  |  Review  |   About  |  Contacts
©2014 Rapid Learning Center. Privacy Policy | Disclaimer
Chemistry Survival Publishing, Biology Survival Publishing and Physics Survival Publishing are the divisions of Rapid Learning Inc
.