(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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simplifying to a Geometric Series

**Physics Forums | Science Articles, Homework Help, Discussion**