Find n(Ni) in Decay Chain with Single Equation

[Big-Daddy]

For the decay chain N₁ -> N₂ -> N₃ -> ... -> N_i -> ... -> N_d, how can I find the amount of particles of N_i, n(N_i), at any point in time t, with a single equation where i can vary from 1 to d? I have already seen WIkipedia's suggestion on the Bateman equations but that method seems to collapse for the case when i=d (as lambda=0 so we'd be dividing by 0).

 

[mfb]

You can use the equation with an additional decay to N_d+1, and take the limit of an infinite lifetime of N_d. Alternatively, subtract all the other elements from the total number of particles.