Let the current be I amperes and the battery be of strength V volts. Let the combined resistance of the three resistors be R ohms.

Therefore, according to Ohm's law, we have

V= IR -----(i)

We know that when the resistors are connected in series, the current is the same in all the resistors. Therefore

V= V₁ +V₂+ V₃ ------------------ (ii)

Let the current flowing through the whole circuit is I, and the equivalent resistance be R.

According to ohm's law

V= IR

V₁= IR₁ -------- (iii)

V₂= IR₂-------- (iv)

V₃= IR₃ ------ (v)

By using eq (i),(ii),(iii) ,(iv) and (v) we get

IR= IR₁+ IR₂+ IR₃

R= R₁+ R₂+ R₃