  The ideal Bose-gas with finite number $N$ of particles is investigated. The
exact expressions for the partition functions and occupation numbers in the
grand canonical, canonical and microcanonical ensembles are found. The
asymp\-totic expressions (in the case $N\gg1$) for the partition functions and
occupation numbers in the canonical and microcanonical ensembles are evaluated.
It is shown that the chemical potential $\mu$ of the ideal Bose-gas can lie in
the range $-\infty<\mu<\infty$ oppositely to the widely adopted opinion that
the value of this potential is negative.
