$L = 1/2$; series converges directly

$L = 1$ (inconclusive); by Raabe's Test with $\lim_{n \to \infty} n(1 - L_n) = 1/2 < 1$, series diverges

$L = 1$ (inconclusive); by Raabe's Test with $\lim_{n \to \infty} n(1 - L_n) = 3/2 > 1$, series converges

Ratio Test does not apply; use Root Test instead