ATAR Notes: Forum

VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: Martoman on April 08, 2010, 01:54:36 am

Title: modulo arithmetic help
Post by: Martoman on April 08, 2010, 01:54:36 am: find the last digit in 1! + 2! + 3!... 2010!

I think this smells like modulo stuff.
Title: Re: modulo arithmetic help
Post by: TrueTears on April 08, 2010, 02:28:18 am: think about mod 10
Title: Re: modulo arithmetic help
Post by: TrueTears on April 08, 2010, 02:36:51 am: Another hint: Consider an easier example:

Find the final decimal digit of 1! + 2! + 3! + ... + 10!.

so we got:

$1!+2!+3!+4! \equiv a+b+c+d \pmod {10}$

So $1! \equiv 1 \pmod {10}$

$2! \equiv -8 \pmod {10}$

$3! \equiv -4 \pmod {10}$

$4! \equiv 24 \pmod {10}$

rest should be a dead giveaway :P