  We investigate the spectrum for partial sums of m position (or gaussian)
operators on monotone Fock space based on $\ell^2(\mathbb{N})$. In the basic
case of the first consecutive operators, we prove it coincides with the support
of the vacuum distribution. Thus, the right endpoint of the support gives their
norm. In the general case, we get the last property for norm still holds. As
the single position operator has the vacuum symmetric Bernoulli law, and the
whole of them is a monotone independent family of random variables, the vacuum
distribution for partial sums of $n$ operators can be seen as the monotone
binomial with $n$ trials. It is a discrete measure supported on a finite set,
and we exhibit recurrence formulas to compute its atoms and probability
function as well. Moreover, lower and upper bounds for the right endpoints of
the supports are given.
