How Does Circuit Resistance Change with Increasing Triangle Numbers?

[Petrulis]

Homework Statement

First of all, there is an an attachment called EXPLANATION which shows the situation and what I have done so far.

So we have got some circuits which are made of triangles (each triangle is made of three resistors (resistors here are shown as rectangles)). The resistance of each resistor is R. The shown part of the circuit is connected to the source with points A and B.

We increse the number of triangles. The first circuit is made of n = 1 triangle, the second circuit has got n = 3 triangles and so on (so n can be equal to 1;3;6;10;15;21...).

I need to find out how the resistance of the circuit depends on n. So I really have to find out the function
(resistance of the circuit) = f(n).

So as you see I can calculate the resistance when n =1;3 and 6, but I stop when I reach n=10.

Homework Equations

Each circuit has got vertical symmetry axis (it is the grey line in the EXPLANATION drawing. This grey line is not the part of the circuit). So the points a, b, c, d, e has got the same potentials, and when we draw the equivalent circuit, we can connect these points with a wire.

The Attempt at a Solution

So I can't draw the equivalent circuit when n = 10, and I can't find out how the resistance of the circuit depends on n.
Maybe I should use other techniques for simplifying the circuit?

Thanks in advance.

 

[Petrulis]

Pleas someone have a look at this problem. It is very important for me.