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Infinite Sequence and Series

From the Basic of Sequences and series you will become Master in Convergent and Divergent series and Much more ...
4.7 (3 ratings)
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1,642 students enrolled
Created by Bharat Hassani
Last updated 8/2015
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  • 37 mins on-demand video
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What Will I Learn?
Basic Idea of Convergent and Divergent Sequences
Limit of Sequences
Increasing, Decreasing and Monotonic Sequences
Bounded Above, Bounded Below and BOUNDED Sequences
Monotonic Sequence Theorem
Convergent and Divergent Series
Partial Sums of Series
Telescoping , Geometric and Harmonic Series
Test for Divergence for Series
Integral Test and P series
Remainder Estimate for the Integral test
Comparison Test and Limit comparison test
Alternating Series Test
Absolute and Conditional Convergent
Ratio and Root Tests
Check Any Type of Series for Convergent OR Divergent
Power Series Representation
View Curriculum
  • Basic Knowledge of Calculus-I topic like Limits, Integral etc.
  • The Calculus II Course on INFINITE SEQUENCE AND SERIES assume that you've got a working knowledge Calculus I, including Limits, Derivatives, and Integration (up to basic substitution). It is also assumed that you have a fairly good knowledge of Trig. Several topics rely heavily on trig and knowledge of trig functions.

This course is not only virtual learning material . You can ask any questions related to Infinite Sequence and series after enrolling in this course.

Here is a listing and brief description of the topics in this course.

  • A brief discussion of sequences. The basic terminology and convergence of sequences.
  • Quick look about monotonic and bounded sequences.
  • Series The Basics we will discuss some of the basics of infinite series.
  • Series Convergence/Divergence about the convergence/divergence of a series
  • Series Special Series Geometric Series, Telescoping Series, and Harmonic Series in this section.
  • Integral Test to determine if a series converges or diverges.
  • Comparison Test/Limit Comparison Test to determine if a series converges or diverges.
  • Alternating Series Test Using the Alternating Series Test to determine if a series converges or diverges.
  • Absolute Convergence A brief discussion on absolute convergence and how it differs from convergence.
  • Ratio Test Using the Ratio Test to determine if a series converges or diverges.
  • Root Test Using the Root Test to determine if a series converges or diverges.
  • Strategy for Series A set of general guidelines to use when deciding which test to use.
  • Estimating the Value of a Series estimating the value of an infinite series.
  • Power Series An introduction to power series and some of the basic concepts.
This course Contains 90% of Video tutorials which include practice section. Master in Sequence and series for your Calculus Course!
  • If you can understand my pronunciation of English in PROMO VIDEO then you can understand all lecture. So Why are you waiting? Click the button "TAKE THIS COURSE".

How much content is included in the course?

Course is updated on Weekly basis and you will get more content in next week.

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What will you know, or be able to do, after completing the course?

Benefits of this course are:

  • After completing this course you will be Master in solving Sequences and series problem of any type.
  • Your teacher will be surprised with your answer.

Who is the target audience?
  • Adult Learner
  • College Students
  • Calculus-I and Calculus-II Students
Students Who Viewed This Course Also Viewed
Curriculum For This Course
Expand All 15 Lectures Collapse All 15 Lectures 36:34
Basic Definition of Sequences
15 Lectures 36:34

Brief Introduction about Course Instructor and Content of the course.

Preview 02:36

Let's start off this section with a discussion of just what a sequence is. A sequence is nothing more than a list of numbers written in a specific order.

Preview 03:29

In this lecture we are given a sequence with particular pattern and we are asked about then general term of the sequence.

How to find the general term of the sequence of pattern given below?

3/5 , -4/25, 5/125, -6/625, 7/3125 .... and so on.

you will come to know how to find general term of sequence.

Preview 02:57

In this lecture you will come to know how to represent the sequence by preceding notation.

we have covered the examples of sequence like [n/(n+1)] and (-1)^n [n+1]/(3^n)

Preview 03:42

In this lecture we will discuss about some sequence like Fibonacci sequence that do not have simple defining equation.

How the Fibonacci sequence made?

Definition by writing out the terms of the sequences

Let us plot graph of sequence like n/(n+1) and check about converges/diverges with the help of graph.

Plotting-Graphing of sequences

Let us discuss about convergent or divergent of any sequence with the help of limit of the sequence.

Limit of Sequence for Convergent or Divergent

Let us draw One more graph of converging sequence. It approaches to single value L.

Example-1 Convergent Sequence

Let us look at Additional example of converging sequence with the help of its graph.

Example-2 Convergent Sequences

In calculus-I we have studied about limit of function but here we will study about limit of sequence.

Let us see the difference in between two definition.

Special theorem for limit of sequence from the definition of limit of function.

Difference between Limit of Function and Limit of Sequences

Let us study about Limit laws of sequences. We have studied in our Calculus-I about Limit laws for the function but here we are going to explore the new limit laws for sequences.

You will surprised that limit laws for sequence is just same as limit laws for function but little difference.

Limit Laws for Sequences same as Limit laws of Function

In calculus, the squeeze theorem (known also as the pinching theorem, the sandwich theorem, the sandwich rule and sometimes the squeeze lemma) is a theorem regarding the limit of a function.

You will study this theorem for Sequences as well.

SQUEEZE Theorem for Sequences

Do you ever think about absolute value of any Sequences? Let us explore it in this lecture.

Theorem: Limit of ABSOLUTE value of Sequence

Let us do sample problem on Limit of Sequences.

Here is the question

(1) Find the limit of [n/(n+1)] as n------> infinity

Sample Problem-1 Limit of Sequences

Let us do sample problem on Convergent/Divergent of Sequences.

Here is the question

(1) Check for the Convergent or Divergent of Sequence


as n------> infinity ?

Sample Problem-2 Convergent or Divergent Sequence
About the Instructor
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Professional Math Tutor , Yoga Trainer , Electrical Engineer

Graduated in Electrical engineering from University of Rajasthan in year 2006, Taught over 1000 students of High school after graduation and still counting, worked as Yoga trainer and trained more than 700 person, Worked as an online tutor for mathematics. Provide coaching to students who prepare India's engineering entrance examination, competitive examination. Published 2 books on calculus, algebra. Prepare Exam papers and question bank based on Entrance exam/test prep after high school, Provide homework help through various freelancing websites, Build strong relationship with students globally to meet their subject requirement and help them to improve their grade and develop their interest in understanding of mathematics.

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