Partial Sums

Is it possible to calculate partial sums in R?

I have the equation:

Px  =  (k / x) * SUM_{from j >= x to infinity} Pj             x=1,2,3,...

where k is a parameter, Pj is the Poisson probability, and x is a rank.
(This is for rank-frequency data.)  In other words, the frequency of an
entity at rank x depends on the sum of frequencies of all entities at
ranks j > x.

Many thanks,
Andrew Wilson