Cannot connect my samsung smart tv to airport extreme, laptop connects fine

If you haven't already, first try temporarily disabling wireless encryption on your 802.11n AirPort Extreme Base Station (AEBSn). If the Samsung TV can now connection wirelessly, reconfigure the AEBSn to use "WPA2 Personal" for the security type.

So how does one disable wireless encryption on the Base Station?

You would do so using the AirPort Utility, as follows: AirPort Utility > Select the AirPort > Manual Setup > AirPort > Wireless tab > Wireless Security = None