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

Linda bought 35 yards of fencing how much did she spend, Linda bought 35 ya...

Linda bought 35 yards of fencing at $4.88 a yard. How much did she spend? To multiply decimals, multiply generally, count the number of decimal places in the problem, then us

Determine the eigenvalues and eigenvectors of the matrix, Determine the eig...

Determine the eigenvalues and eigenvectors of the subsequent matrix. Solution : The first thing that we require to do is determine the eigen-values. It means we require

Sum of their areas is given find radii of the two circles, Two circles touc...

Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:

Geometry, I don''t get it .... Help

I don''t get it .... Help

Standardization of variables, Standardization of Variables - Before we...

Standardization of Variables - Before we use the general distribution curve to determine probabilities of the continuous variables, we require standardizing the original units

Quadratic equation, What do we mean by the roots of a quadratic equation ?

What do we mean by the roots of a quadratic equation ?

Find the perameter of square in maths, Find the perameter of SQUARE in math...

Find the perameter of SQUARE in maths? Remember that in a square, all sides are of equal length. A square is also a kind of rectangle. So, you can use length (l) times width

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