I have an example from Stewart's Calculus where the equation $y'' + y = 0$ is solved using power series. The equation
Subscript[c, 2 + n] == -(Subscript[c, n]/((n + 1) (n + 2)))
is used to determine the coefficients recursively and is straightforward to solve "by hand", but I cannot see how to do this in Mathematica. Searching for "Recursion Relation" in the Wolfram Language & System Documentation Center returns a tutorial Functions That Remember Values They Have Found, which uses the example of a Fibonacci function
f[x_] := f[x] = f[x - 1] + f[x - 2]
f = f = 1
I have followed this example to input a function to calculate the coefficients recursively, but whatever I try I get a
$RecursionLimit error. I would be grateful if someone could explain how to enter such a function since I am clearly misunderstanding the basic concept behind this in some way.