Background

- System of points a, b, c and q

- a, b, and c exert a push on q moving it to the end of a vector that is 2 times the vector from a, b, or c to q.

- a, b, and c do this at the same time, after each cycle the x and y values of q are the average of the end points of the vectors.

- This happens n times

First derivation

The final x value is the sum of the averages of all the vectors endpoints divided by the number of iterations so n.

Same goes for y

I further thought why keep it at intervals when it can be a constant force.

From this I derived

The integral from 1 to n of the average of the averages of the vector endpoints in respect to the x value of q.

Same for y

Hope I wasn't too vague with it but am I at least close to right?

Also how do I insert equations?

This wasn't homework by the way don't rage at me.