A CRJ200 CAPT REPORTS BEING SO FATIGUED AFTER A 6 DAY 29 HR 33 MIN TRIP THAT HE FAILED TO REMOVED ELECTRICAL POWER AND SECURE THE ACFT BEFORE GOING HOME.

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I WAS NOTIFIED BY THE CREW WHO LATER CAME TO THE ACFT AFTER I LEFT TO GO HOME THAT I HAD LEFT THE EXTERNAL PWR ON THE ACFT. I HAD JUST COMPLETED A 6 DAY; 29 HR AND 33 MIN TRIP. I WAS EXTENDED TWICE ON THIS TRIP. THE FIRST TIME AT THE END OF THE 4TH DAY; AND AGAIN ON THE 6TH DAY FOR ONE MORE 'LOW STRESS OUT AND BACK TO ZZZ.' WELL; THE LAST OUT AND BACK WAS TO ZZZ1. ADDITIONALLY; I FLEW IT WITH A FO WHO HAD LESS THAN 100 HRS IN THE CRJ AND HAD NEVER BEEN TO ZZZ1. WITH THIS AS BACKGROUND; WE DEPARTED FOR ZZZ1. THANKFULLY; THE OUT AND BACK TO ZZZ1 WENT FLAWLESSLY! WHEN WE PULLED UP TO THE GATE AND SHUT DOWN THE ENGS; I LET OUT A HUGE SIGH OF RELIEF. THE 6 DAY TRIP FROM HELL WAS OVER! I COMPLETED THE PARKING CHKLIST AND BEGAN TAKING THE CREW BAGS OFF THE ACFT. THE FO COMPLETED THE POSTFLT AND WENT HOME. I TALKED TO THE FLT ATTENDANT FOR A FEW MINS; SHE WAS GOING TO FLY THE SAME ACFT TO ZZZ2 (THAT'S WHAT I REMEMBER ANYWAY) WITH A NEW FLT CREW. I SAID GOODBYE AND THEN LEFT THE ACFT TO SIGN-OUT AND GO HOME. WHAT I FORGOT TO DO WAS THE TERMINATING CHKLIST. THIS PAINFULLY OBVIOUS OVERSIGHT WAS CAUSED BY MY FATIGUE; CAUSING THE ERRONEOUS CONCLUSION THAT SINCE THE FLT ATTENDANT WAS ON BOARD; THE 'FLT CREW' WAS PRESENT AND I COULD GO HOME. I NEVER GAVE IT A SECOND THOUGHT ABOUT THE CONFIGN OF THE ACFT (IE; THE EXTERNAL PWR WAS STILL POWERING THE ACFT). BEYOND A SHADOW OF A DOUBT THIS MISTAKE WAS A DIRECT RESULT OF FATIGUE. I WAS SO TIRED THAT GOOD JUDGMENT AND CHKLIST DISCIPLINE WAS REPLACED WITH FAULTY JUDGMENT AND CHKLIST COMPLIANCE. BOTTOM LINE: IT AIN'T OVER UNTIL IT'S OVER! REGARDLESS OF HOW TIRED YOU ARE! OR IN PILOTESE: 'TERMINATION CHKLIST -- COMPLETE.