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 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 non-recursive 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 non-recursive form for the odd sequence and to determine the radii of convergence.

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