Prove the average external force is Zero

[Manolisjam]

1.Problem statement
Prove the average external force of a system of particles N starting from rest and ending at rest is zero.

Homework Equations

If the system moves periodically prove the av. external force is zero in a period

The Attempt at a Solution

I don't quite understand what i am asked .Since i don't have a definition for a average force of a system of particles. Yet i tried to derive the eq for momentum of a system.So this is the momentum of the system i found. Now i know that going from rest to rest change of momentum must be zero . But i have internal and external forces. So don't know how to proceed

 

[BvU]

There is someething with internal forces you need to exploit here. has to do with one of the Newton laws...:
what is the effect of an internal force on the motion of the system ?

 

[Manolisjam]

There is someething with internal forces you need to exploit here. has to do with one of the Newton laws...:
what is the effect of an internal force on the motion of the system ?

Its zero the rest of the math is ok? SO the double sum is zero.

 

[BvU]

Can't read the small writing. What I hinted at is action = - reaction so the internal forces can't influence the center of mass of the system