Power series - sequences and series, Mathematics

Assignment Help:

Power Series

We have spent quite a bit of time talking about series now and along with just only a couple of exceptions we've spent most of that time talking about how to find out if a series will converge or not.  It is now time to start looking at some particular types of series and we'll eventually reach the point in which we can talk about a couple of applications of series.

 In this part we are going to start talking regarding power series.  A power series regarding to a, or just power series, is any type of series that can be written in the form, in which a and cn are numbers.  The cn's are frequently called the coefficients of the series.  The 1st thing to notice about a power series is that it is a function of x.  That is dissimilar from any other kind of series that we have looked at to this point.  In all the prior segments we've only allowed numbers in the series and now we are permit variables to be in the series also.  Though, this will not alter how things work.  All that we know about series still holds. 

In the conversation of power series convergence is still a main question that we'll be dealing with. The variation is that the convergence of the series will now relies on the values of x that we put into the series. A power series might converge for some values of x and not for another value of x.  Before we get too far into power series there is some terminology that we need to get out of the way.


Related Discussions:- Power series - sequences and series

How much did kara pay in interest, Kara borrowed $3,650 for one year at an ...

Kara borrowed $3,650 for one year at an annual interest rate of 16%. How much did Kara pay in interest? To ?nd out 16% of $3,650, multiply $3,650 through the decimal equivalent

Diffrential integral , All the integrals below are understood in the sense ...

All the integrals below are understood in the sense of the Lebesgue. (1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]

Exact differential equations, The subsequent type of first order differenti...

The subsequent type of first order differential equations which we'll be searching is correct differential equations. Before we find in the full details behind solving precise diff

Permutations and Combinations, How many 4 digit number lass than 6000 can b...

How many 4 digit number lass than 6000 can be made with the digits 7,6,4 and 2 if digits are not repeated?

Trignometry, Define the given satatement : 1.sin90-sin89=sin10 using pythag...

Define the given satatement : 1.sin90-sin89=sin10 using pythagoras theoram 2. How can any value of sin and cosis always given any value of cosec.

Linear programming, Maximize P=3x+2y Subject to ...

Maximize P=3x+2y Subject to x+y =6 x =3 x =0,y =0

Analytical geometry, convert the equation 4x^2+4y^2-4x-12y+1=0 to standard ...

convert the equation 4x^2+4y^2-4x-12y+1=0 to standard form and determine the center and radius of the circle. sketch the graph.

Explain the common forms of linear equations, Explain the Common Forms of L...

Explain the Common Forms of Linear Equations ? An equation whose graph is a line is called a linear equation. Here are listed some special forms of linear equations. Why should

Find intervals while function is increasing or decreasing, Find out all int...

Find out all intervals where the given function is increasing or decreasing. f ( x ) = - x 5 + 5/2 x 4 + 40/3 x 3 + 5 Solution To find out if the function is increasi

Find the number of students in the class, Students are made to stand in row...

Students are made to stand in rows. If one student is extra in a row there would be 2 rows less. If one student is less in a row there would be 3 rows more. Find the number of stud

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