What is remainder from division of $A$ by $10$? $A=0!+3!+6!+9!+…+81!$
I thought I was kind of expert in high school mathematics until I was hit in punch by my brother who is in secondary school. Guys I will really appreciate if anyone can get me out of this mess.
$6!, 9!, 12!, ... 81!$ will all end in 0 since they each a 5 and a 2 as factors. So to find the units place, just look at $0! = 1$ and $3! = 6$. So your units place for the sum will be $1 + 6 + 0 + 0 + 0 + ... + 0 = 7$. And there's your remainder.