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Find the last two digits of the following sum: \(5! + 10! + 15! + \cdots + 100!\)

 Apr 21, 2020
 #1
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All you have to do is to sum first 7-8 terms and you will end up with 80 for the last 2 digits.

 Apr 21, 2020
 #2
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All the terms from 10! have  2*5*10 = 100 as a factor so none of these will affect the last 2 places in the sum

 

So I only need the last 2 places of 5!

The last place will be 0  (2*5)

 

1*2*3*4*5 = 120 

So the last 2 digits are 20

 Apr 22, 2020

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