I am trying to find the last hexadecimal digit of a series of large factorials, but I'll start with 990! + 991! +...+1000!. I am trying to find the last hex digit of a larger sum than this, but I think all I need is a push in the right direction, because right now I am lost.
Where would I even begin? I tried to convert 1000 to hexadecimal form -- 3E8 -- but that didn't seem to help me at all, or at least not as much as I thought it would.
Any and all help is greatly appreciated.