Mathematics  >  Algebra for IIT JAM Mathematics  >  Binomial Series

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

Document Description: Binomial Series for Mathematics 2022 is part of Algebra for IIT JAM Mathematics preparation. The notes and questions for Binomial Series have been prepared according to the Mathematics exam syllabus. Information about Binomial Series covers topics like and Binomial Series Example, for Mathematics 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Binomial Series.

Introduction of Binomial Series in English is available as part of our Algebra for IIT JAM Mathematics for Mathematics & Binomial Series in Hindi for Algebra for IIT JAM Mathematics course. Download more important topics related with notes, lectures and mock test series for Mathematics Exam by signing up for free. Mathematics: Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics
1 Crore+ students have signed up on EduRev. Have you?

In this final section of this chapter we are going to look at another series representation for a function.  Before we do this let’s first recall the following theorem.

Binomial Theorem
If n is any positive integer then,

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

where, 

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

This is useful for expanding (a+b)n for large n when straight forward multiplication wouldn’t be easy to do.  Let’s take a quick look at an example.

Example 1 Use the Binomial Theorem to expand (2x−3)4

Solution. There really isn’t much to do other than plugging into the theorem.

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

Now, the Binomial Theorem required that n be a positive integer.  There is an extension to this however that allows for any number at all.

Binomial Series

If k is any number and |x|<1 then, 

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

So, similar to the binomial theorem except that it’s an infinite series and we must have |x<1 in order to get convergence.
Let’s check out an example of this.

Example 2 Write down the first four terms in the binomial series for  √9−x

Solution. So, in this case Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics and we’ll need to rewrite the term a little to put it into the form required. 

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

The first four terms in the binomial series is then,

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

The document Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics is a part of the Mathematics Course Algebra for IIT JAM Mathematics.
All you need of Mathematics at this link: Mathematics
Download as PDF

Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!

Related Searches

mock tests for examination

,

Viva Questions

,

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

,

Summary

,

past year papers

,

practice quizzes

,

Semester Notes

,

video lectures

,

Objective type Questions

,

Free

,

Extra Questions

,

study material

,

Important questions

,

Sample Paper

,

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

,

MCQs

,

Exam

,

Previous Year Questions with Solutions

,

Binomial Series Notes | Study Algebra for IIT JAM Mathematics - Mathematics

,

shortcuts and tricks

,

pdf

,

ppt

;