Resistors in series
Example 1 is 2 resistors in series
2 resistors in series
In this example the total resistance (RT) = R1 + R2. So in the example above its 10k + 10k = 20k
Now 3 resistors in series as demonstrated in the image below
3 resistors in series
In this example the total resistance (RT) = R1 + R2 + R3. So in the example above its 10k + 10k + 10k = 30k
Resistors in parallel
2 resistors in parallel
If two 10k resistors are connected in parallel like above, the combined resistance would be 1/[(1/10000) + (1/10000)] = 5000 ohms or 5k
3 resistors in parallel
If three 10 K resistors are connected in parallel like the image above, then using the equation shown here one would workout that the combined resistance is about 3333 ohms or about 3k3.
When resistors are connected in parallel, the combined value is arrived at by adding the reciprocal of the value of the individual resistors. The reciprocal of this is the new value.In the above example, this would be
$$
\frac{1}{R_e} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_N}
$$