SOLUTION: 1!+2!+3!+....+100! divide by 5?

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Question 949378: 1!+2!+3!+....+100! divide by 5?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
5%21=1%2A2%2A3%2A4%2A5 is divisible by 5 . In other words,
5%21%2F5=1%2A2%2A3%2A4%2A5%2F5=1%2A2%2A3%2A4=4%21=24 is an integer.
The same is true about the factorials of every number greater than 5 .
In other words, if k is a positive integer and k%3E5 ,
k%21%2F5 is a positive integer.
So, in the case of ,
we know that all the terms except the first term are positive integers.
What about that first %281%21%2B2%21%2B3%21%2B4%21%29%2F5 term?

is not an integer.
When you divide 1%21%2B2%21%2B3%21%2B4%21 by 5 you get
an integer quotient, 6 , and a remainder, 3 .
The same happens when you divide 1%21%2B2%21%2B3%21%2B%22....%22%2B100%21 by 5 :
you get an integer quotient, and 3 for a remainder.