Ratio test
Theorem 5.2 (Ratio test). If \(a_n \neq 0\) for all large \(n\) and \(L = \lim _{n \to \infty } \abs {a_{n+1}/a_n}\) exists in \([0, \infty ]\), then the radius of convergence of \(\sum a_n (z - z_0)^n\) is \(R = 1/L\).
Source: [1, ch. 5]
Theorem 5.2 (Ratio test). If \(a_n \neq 0\) for all large \(n\) and \(L = \lim _{n \to \infty } \abs {a_{n+1}/a_n}\) exists in \([0, \infty ]\), then the radius of convergence of \(\sum a_n (z - z_0)^n\) is \(R = 1/L\).
Source: [1, ch. 5]