SOLUTION: Find the units digit of the sum,$$ 1! + 2! + 3! + \cdots + 2006!. $$(latex) Find the units digit of the sum, 1! + 2! + 3! + ... + 2006!.(not latex) I am stuck. I cannot find a pa

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Question 1169664: Find the units digit of the sum,$$ 1! + 2! + 3! + \cdots + 2006!. $$(latex)
Find the units digit of the sum, 1! + 2! + 3! + ... + 2006!.(not latex)
I am stuck. I cannot find a pattern because of the high numbers that this problem goes to. I have spent a lot of time, but haven't got anything. Thank you.
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.


            From the first glance, the problem seems to be hard,  but . . . actually . . . it is a joke problem. 


As soon as the last digit of n! is zero, it does not influence more on  the last digit of the sum . . . 


So, the last requested digit comes from

    1! + 2! + 3! + 4! + 5! = 1 + 2 + 6 + 24 + 120 


and is,  T H E R E F O R E,   3.


ANSWER.  The last digit of  1! + 2! + 3! + . . .  + 2006!   is   .

Solved.



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