Bug introduced in 10.0.1 and fixed in 12.0.0
Version 11.2.0.0 on MacBook Pro:
w[n_] := 2^(-1 + n) QPochhammer[-1, 3/2, n]
Print["Auto: ", SumConvergence[w[n], n]]
Print["Ratio: ", SumConvergence[w[n], n, Method -> "RatioTest"]]
Yields True and False respectively. Auto is apparently wrong as suggested by:
ListPlot[Log[Table[w[n], {n, 1, 100}]]]
and also by hand-calculating the ratio test.
bugs
tag. $\endgroup$