- #1
xago
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Homework Statement
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...
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