(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a question with asks to solve a differential equation via power series and I've done everything up to finding the recurrence relation which is a[itex]_{n+2} = -[/itex][itex]\frac{a_{n}}{n+2}[/itex]

Given the initial conditions a[itex]_{o}[/itex] = 1 and a[itex]_{1}[/itex] = 0 I'm trying to simplify the series into a geometric series. The series is 1,-1/2, 1/8, -1/48, 1/480, -1/5760 etc...

3. The attempt at a solution

So far I've gotten (-1)[itex]^{n}[/itex] in the numerator to account for the alternating negative sign, however I can't find the denominator for the life of me...

my best attempt is [itex]\frac{(-1)^{n}}{(2^n)}[/itex] but it only works for the first 2 terms :S

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# Homework Help: Simplifying to a Geometric Series

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