  The superradiant stability of five and six-dimensional extremal
Reissner-Nordstrom black holes under charged massive scalar perturbation is
studied. In each case, it is analytically proved that the effective potential
experienced by the scalar perturbation has only one maximum outside the black
hole horizon and no potential well exists for the superradiance modes. So the
five and six-dimensional extremal Reissner-Nordstrom black holes are
superradiantly stable. In the proof, we develop a new method which is based on
the Descartes' rule of signs for the polynomial equations. Our results
generalize the previous study that four-dimensional extremal Reissner-Nordstrom
black hole is superradiantly stable under charged massive scalar perturbation.
