What was found
LEFT ENGINE ENGINE VIBRATION: ON CLIMBOUT THROUGH FL250 WE FELT ENGINE VIBRATIONS AND WE HEARD A MUFFLED BANG. WE THEN RECEIVED CAS MESSAGES ABOUT ENGINE EXCEEDENCE AND NO DISPATCH, THEN ENGINE 1 FAILURE AND WE SMELLED SOMETHING BURNING THAT WENT AWAY AFTER WE SECURED THE ENGINE. WE RAN THE ENGINE FAILURE QRH, THEN DECIDED TO NOT RUN THE ENGINE RESTART QRH BECAUSE N2 WAS INDICATION 0.0%. AS WE DESCENDED INTO WARMER AIR, N2 CLIMBED TO 4.0%. ON POSTFLIGHT, I NOTED THAT THE L ENGINE OIL LEVEL WAS NOT VISIBLE IN THE SIGHT GAUGE. REMOVED LT ENGINE. PERFORMED ALL REQUIRED ENGINE RUN/LEAK CHECKS WITH NO DEFECTS NOTED. ALL MAINTENANCE PERFORMED IAW AMM 71-00-00 & EMM 71-00-00.