Multiple Maneuvers
Because the mass ratios apply to any given burn, when multiple maneuvers are performed in sequence, the mass ratios multiply.
Thus it can be shown that, provided the exhaust velocity is fixed, this means that delta-vs can be added:
When M1, M2 are the mass ratios of the maneuvers, and V1, V2 are the delta-v's of the first and second maneuvers
Where V = V1 + V2 and M = M1 M2.
Which is just the rocket equation applied to the sum of the two maneuvers.
This is convenient since it means that delta-vs can be calculated and added and the mass ratio calculated only for the overall vehicle for the entire mission. Thus delta-v is commonly quoted rather than sequences of mass ratios.
Read more about this topic: Delta-v
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