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

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

how to make a tape diagram and a equivalent ratio

Project, report on shares and dovidend using newspaper

report on shares and dovidend using newspaper

Times fractons, In a garden, 1/8 of the flowers are tulips. 1/4 of the tuli...

In a garden, 1/8 of the flowers are tulips. 1/4 of the tulips are red. What fraction of the flowers in the garden are red tulips?

Find out the mean time, 1 . The probability that a couple will have a child...

1 . The probability that a couple will have a child with black hair is 0.6. If this couple has 7 children what is (a) the probability that exactly 3 of these children have bl

How many points did he score during his senior year, Michael scored 260 poi...

Michael scored 260 points during his junior year on the school basketball team. He scored 20% more points during his senior year. How many points did he score during his senior yea

Solving Trig Equations, How would you solve the equation: 1+ sin(theta)= 2 ...

How would you solve the equation: 1+ sin(theta)= 2 cos^2(theta)?

Abstract algebra, Let D(subscript12) = ({x,y : x^2 = e ; y^6 = e ; xy =(...

Let D(subscript12) = ({x,y : x^2 = e ; y^6 = e ; xy =(y^-1) x}) a) Which of the following subsets are subgroups of D(subscript12) ? Justify your answer. i) {x,y,xy,y^2,y^3,e}

Proof of alternating series test, Proof of Alternating Series Test With...

Proof of Alternating Series Test With no loss of generality we can assume that the series begins at n =1. If not we could change the proof below to meet the new starting place

Determine a trigonometric function, At rest, the human heart beats once eve...

At rest, the human heart beats once every second. At the strongest part of the beat, a person's blood pressure peaks at 120mmHg. At the most relaxed part of the beat, a person's bl

Area related to circle, If ABCD isaa square of side 6 cm find area of shad...

If ABCD isaa square of side 6 cm find area of shaded region

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