Find a power series representation for the function, Mathematics

Assignment Help:

Find a power series representation for the subsequent function and find out its interval of convergence.

g (x) = 1/1+x3

Solution

What we require to do here is to relate this function back to f (x) = 1/ (1-x). In fact this is easier than it might look. Remind that the x in f (x) = 1/ (1-x) is simply a variable and can represent anything. Thus, a quick rewrite of g(x) gives,

g (x) = 1/ 1- (-x3)

and so the - x3 in  g (x) holds the same place as the x in f (x) = 1/ (1-x). Therefore, all we need to do is replace the x in

181_Find a power series representation for the function 1.png

and we've got a power series representation for g (x).

1498_Find a power series representation for the function 2.png

Note: we replaced both the x in the power series and in the interval of convergence. 

All we need to do now is a modest simplification.

7_Find a power series representation for the function 3.png

Thus, in this case the interval of convergence is similar as the original power series.  This generally won't happen. Much more frequently, than not the new interval of convergence will be dissimilar from the original interval of convergence.


Related Discussions:- Find a power series representation for the function

Application of interpolation and extrapolation, Application Interpolati...

Application Interpolation and extrapolation are widely used by businessmen, administrators, sociologists, economists and financial analysts. While interpolation hel

Contravariant vector, Ask question #suppose that components of a contravari...

Ask question #suppose that components of a contravariant vector A^i (for n=3)in the coordinate system (x^1,x^2,...,x^n) are A=x,A=y,A=z.Find the components A^p of the vector in the

Ratio, how to make a tape diagram and a equivalent ratio

how to make a tape diagram and a equivalent ratio

Java program for sorting algorithms, Introduction: In this project, yo...

Introduction: In this project, you will explore a few sorting algorithms. You will also test their efficiency by both timing how long a given sorting operation takes and count

Marketing plan and its parts, can you offer help with an entry level market...

can you offer help with an entry level marketing class and with developing charts and tables for the final marketing plan?

Formula to calculate the surface area of basketball, Keith wants to know th...

Keith wants to know the surface area of a basketball. Which formula will he use? The surface area of a sphere is four times π times the radius squared.

Calculate the value of the following limits, Calculate the value of the fol...

Calculate the value of the following limits. Solution To remind us what this function such as following the graph. hence, we can see that if we reside to the r

Pair of straight line, a pair of straight lines are drawn through the origi...

a pair of straight lines are drawn through the origin forms with the line 2x+3y=6 an isoceles triangle right angled at origin find the equation of pair of straight line?

How many rolls will she required to purchase, Karen is buying a wallpaper b...

Karen is buying a wallpaper border for her bedroom, that is 12 ft by 13 ft If the border is sold in rolls of 5 yards each, how many rolls will she required to purchase? The dis

Population problem - nonhomogeneous systems, The next kind of problem seems...

The next kind of problem seems as the population problem. Back in the first order modeling section we looked at several population problems. In such problems we noticed a single po

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd