
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 7th, 2017, 06:29 PM  #1 
Member Joined: Feb 2014 Posts: 91 Thanks: 1  Power Series
question 12 I need to find two linearly independent power series and radius of convergence. This test is coming very soon. The class is accelerating due to missed school days and I need to be really ready. Am I on the right track with this problem? 
April 7th, 2017, 07:40 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,381 Thanks: 1278 
Solving this you get two sequences corresponding to the even and odd terms of $a_{n+2}=\dfrac{4}{(n+2)(n+1)}a_n$ The even sequence depends on $a_0$, the odd on $a_1$ You can compute nonrecursive formulas for these two sequences to determine the radius of convergence. the even sequence for example is $a_{k}=\dfrac{4^k}{(2 k)!}a_0,~k=0,1,2,\dots$ (I've reindexed it) I leave you to compute the nonrecursive form for the odd sequence and to determine the radii of convergence. 

Tags 
power, series 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Sum of power series  Mrto  Calculus  3  April 27th, 2015 02:23 PM 
power series  bonildo  Calculus  5  December 6th, 2014 08:22 AM 
Power Series  Diehardwalnut  Math Books  0  October 13th, 2014 06:47 PM 
In need of help disk, series test, taylor, and power series  g0bearmon  Real Analysis  2  May 22nd, 2012 12:10 PM 
In need of help disk, series test, taylor, and power series  g0bearmon  Calculus  1  December 31st, 1969 04:00 PM 