theorem :: CLVECT_3:31

for X being ComplexUnitarySpace
for seq being sequence of X
for Rseq being Real_Sequence st ( for n being Nat holds seq . n <> 0. X ) & ( for n being Nat holds Rseq . n = ||.(seq . (n + 1)).|| / ||.(seq . n).|| ) & Rseq is convergent & lim Rseq > 1 holds
not seq is summable