When resistors are connected in series does total resistance decrease or increase?

Hello!
The answer is increases. Now let's figure out why.
Ohm's law states that the current through a conductor is directly proportional to the voltage, or, in other words, that the voltage drop between endpoints of a conductor is directly proportional to the current, Delta U = I R. The constant R is called the resistance of the conductor.
When some n resistors of the resistances R_i are connected in series, the same electrical current I flows successively through each of them. And each resistor causes the voltage drop proportional to its resistance R_i:  Delta U_i = R_i I. Together, all resistors cause the voltage drop of (R_1 + R_2 + ... + R_n) I, which, in turn, means that the total resistance of a chain is R_1 + R_2 + ... + R_n.
Note that a resistance is always positive, so a sum is always greater than any summand.