Basic maths: 10k? resistor, 5V voltage, 100µF cap=0.76 second LED fadeout

"Question is what happened to the missing .25 joules of energy?"

During the time that current flowed from one capacitor into the next capacitor, a magnetic field was changed. The energy went into that magnetic field during an impulse. A resonance then occurs without damping, and the oscillation lasts forever. The missing energy is tossed about forever, outside of the capacitive energy.