Ladder Network:
A ladder network is a type of electrical circuit that consists of a series of resistors connected in both series and parallel configurations. The resistors are arranged in a ladder-like pattern, hence the name ladder network. The ladder network is commonly used in electronic circuits for various purposes such as voltage division, impedance matching, and filter design.

Equivalent Resistance Calculation:
To find the equivalent resistance of a ladder network, we need to simplify the circuit by combining resistors in series and parallel. Here, we have a ladder network with resistors of 1 ohm, 2 ohms, 3 ohms, 4 ohms, 5 ohms, and 6 ohms. Let's calculate the equivalent resistance step by step.

Step 1: Identifying the Series and Parallel Groups:
To simplify the ladder network, we need to identify the resistors that are connected in series and parallel.

- The 1-ohm resistor is connected in series with the 2-ohm resistor.
- The 3-ohm resistor is connected in series with the 4-ohm resistor.
- The 5-ohm resistor is connected in series with the 6-ohm resistor.

Step 2: Combining Series Resistors:
In series connection, the total resistance is the sum of individual resistances.

- The 1-ohm and 2-ohm resistors are in series. Their total resistance is 1 + 2 = 3 ohms.
- The 3-ohm and 4-ohm resistors are in series. Their total resistance is 3 + 4 = 7 ohms.
- The 5-ohm and 6-ohm resistors are in series. Their total resistance is 5 + 6 = 11 ohms.

Step 3: Combining Parallel Resistors:
In parallel connection, the reciprocal of the total resistance is equal to the sum of the reciprocals of individual resistances.

- The 3-ohm and 7-ohm resistors are in parallel. Their total resistance is 1 / (1/3 + 1/7) = 2.1 ohms.
- The 5-ohm and 11-ohm resistors are in parallel. Their total resistance is 1 / (1/5 + 1/11) = 3.55 ohms.

Step 4: Combining the Remaining Series Resistors:
The remaining resistors, which are 2.1 ohms and 3.55 ohms, are connected in series. Their total resistance is 2.1 + 3.55 = 5.65 ohms.

Result:
Therefore, the ladder network with resistors of 1 ohm, 2 ohms, 3 ohms, 4 ohms, 5 ohms, and 6 ohms has an equivalent resistance of 5.65 ohms.