  Tachyon condensation in the open bosonic string is analyzed using a
perturbative expansion of the tachyon potential around the unstable D25-brane
vacuum. Using the leading terms in the tachyon potential, Pad\'e approximants
can apparently give the energy of the stable vacuum to arbitrarily good
accuracy. Level-truncation approximations up to level 10 for the coefficients
in the tachyon potential are extrapolated to higher levels and used to find
approximants for the full potential. At level 14 and above, the resulting
approximants give an energy less than -1 in units of the D25-brane tension, in
agreement with recent level-truncation results by Gaiotto and Rastelli. The
extrapolated energy continues to decrease below -1 until reaching a minimum
near level 26, after which the energy turns around and begins to approach -1
from below. Within the accuracy of this method, these results are completely
consistent with an energy which approaches -1 as the level of truncation is
taken to be arbitrarily large.
