How is resistance different in series and parallel and why does parallel give less resistance?

In a series connection, the same current flows through every resistor one after another, and the total resistance is just the sum: R = R1 + R2 + R3. Adding a resistor always increases the total because the current has to push through more obstacles in a single path. In a parallel connection, each resistor offers a separate path for the current, and the total resistance is found from 1/R = 1/R1 + 1/R2 + 1/R3. Adding more parallel resistors gives the current more lanes to flow through, like opening extra doors in a crowded hall, so the overall opposition drops and the total resistance becomes smaller than even the smallest individual resistor. Remember: series adds up, parallel always gives less than the smallest resistor.