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Consider the
particles having masses
each and moving with velocities
each, where 
Then the net momentum:-
or,
The velocity of the center of mass of these particles,
Now consider the single particle whose mass is the sum of masses of those
particles.
and this particle is moving with the velocity of the center of mass of the particles.
Then, momentum of this single particle,
From (2),
and from (1), we get,
Hence the Proof!
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☘️ See the attachment picture for Explanation.
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