AK_Kadaveru
Posts : 28
Join date : 2009-10-20
 | | Subject: adding factorials Sat Nov 28, 2009 3:48 pm | |
| what is the right most digit of 0!+1!+2!+3!+4!................999,999,999,999,998!+999,999,999,999,999!+1,000,000,000,000,000!? | |
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BhandarkarA
Posts : 85
Join date : 2009-09-11
| | Subject: Re: adding factorials Tue Dec 29, 2009 4:25 pm | |
| - AK_Kadaveru wrote:
- what is the right most digit of 0!+1!+2!+3!+4!................999,999,999,999,998!+999,999,999,999,999!+1,000,000,000,000,000!?
Hello, With n! defined as n x n-1 x n-2...x2x1, we notice that the units digit of any factorial where n>4 is zero. For example, 5! is 12 0, 6! is 72 0, and so on. The reason why is that every integer n beyond our domain of [0,4] has a factorial divisible by 10 (the factorial will contain both 2 and a 5 which multiply to 10.) So, the question becomes what factorials do we need to consider that will affect the units digit. The answer: every factorial less than 5! 0!+1!+2!+3!+4!= 1+1+2+6+24= 34 Thus we have units digit of 4 as our final answer. Archis R. Bhandarkar | |
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AK_Kadaveru
Posts : 28
Join date : 2009-10-20
| | Subject: Re: adding factorials Wed Dec 30, 2009 8:06 pm | |
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