Answer:
-m × (vector from center to the fixed vertex)
Step-by-step explanation:
The sum of concern is the sum of difference vectors (vn-vf), where vn is the vector from center to vertex n, and vf is the fixed vertex.
This sum can be divided into two parts:
... ∑[n=1..m](vn -vf) = ∑[n=1..m]vn - m(vf)
Sine the polygon is regular the sum of vectors from its center to each vertex is zero, so this sum reduces to ...
... 0 -m(vf)
... = -m × (vector from center to fixed vertex)
