Radius and interval of convergence

dcrisci
Messages
45
Reaction score
0

Homework Statement



infinity
∑ (x^(n+5))/3n! Find the radius of convergence and interval of convergence
n=0

Homework Equations


The Attempt at a Solution



I got 0 for the radius and 0 for the interval of convergence using the ratio test. This is no right. Can someone please help me? Thank you
 
Physics news on Phys.org
dcrisci said:

Homework Statement



infinity
∑ (x^(n+5))/3n! Find the radius of convergence and interval of convergence
n=0

Homework Equations





The Attempt at a Solution



I got 0 for the radius and 0 for the interval of convergence using the ratio test. This is no right. Can someone please help me? Thank you


Show your work.
 
Answer

Here it is
 

Attachments

  • IMG_3367.jpg
    IMG_3367.jpg
    14.6 KB · Views: 426

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Interval of convergence of power series from ratio test
Replies
2
Views
1K
Ratio Test vs AST
Replies
4
Views
1K
Interval of uniform convergence of a series
Replies
24
Views
3K
Intervals of Convergence- Power Series
Replies
11
Views
3K
Proving convergence of rational sequence
Replies
2
Views
1K
A problem with the convergence of a series
Replies
5
Views
2K
Is the Interval of Convergence for (x-2)^n / n^(3n) from -1 to 5?
Replies
2
Views
1K
Valid conclusion for an absolutely convergent sequence
Replies
4
Views
996
On the ratio test for power series
Replies
2
Views
2K
Finding Convergence Radius & Interval: Solving a Complex Homework Problem
Replies
2
Views
970

Hot Threads

Recent Insights

Back
Top