The last digit of (1!+2!+…+2005!)500 is

N=1!+2!+⋯+2005!=(1!+2!+3!+4!)+(5!+⋯+2005!)    = 33 + an integer having 0 in its unit's place    = an integer having 3 in its unit's placeHence, N500 is an integer having 1 in its unit's place.