An object moves at speed v1/c ? ?1 with respect to S1, which moves at speed ?2 with respect to S2, which moves at speed ?3 with respect to S3, and so on, until finally SN??1 moves at speed ?N with respect to SN (see Figure). Show that the speed, ?(N), of the object with respect to SN can be written as

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S1 S2 S3 S4 S5 P - PN BIN) P + PN (10.73) %3D where ПО- 6). PN = II(1+Bi), and (10.74) i=1 i=1 .... S....