Question

The remainder when $2!+4!+6!+8!+...+50!$ is divided by $18$ is

Answer 1

Here, $6!=6\times 5\times 4\times 3\times 2\times 1$
It is divisible by $18$
$\therefore (6!+8!+...50!)$ will be divisible by $18$
$\therefore 2!+4!+6!+8!+...+50!=2!+4!+18k=2+24+18k=26+18k=18(k+1)+8$
$\therefore$ the remainder is $8$