  We propose a simple and efficient way to compute quasinormal frequencies of
spherically symmetric black holes. We revisit an old idea that relates them to
bound state energies of anharmonic oscillators by an analytic continuation.
This connection enables us to achieve remarkable high-order computations of WKB
series by Rayleigh-Schr\"odinger perturbation theory. The known WKB results are
easily reproduced. Our analysis shows that the perturbative WKB series of the
quasinormal frequencies turn out to be Borel summable divergent series both for
the Schwarzschild and for the Reissner-Nordstr\"om black holes. Their Borel
sums reproduce the correct numerical values.
