Question

What is the unit digit of sum $2!+3!+4!+.....+22!$

Answer 1

Unit digital of all $n!$ for $n\ge 5$ is zero(0).
Therefore the term $2!+3!+4!$ will decide unit place
$2!+3!+4!=2+6+24=32$
Therefore unit place of the sum
${\sum }_{n=2}^{22}n!=2$