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

 Feb 12, 2021
 #1
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I'm guessing they would both be 0

 Feb 12, 2021
 #2
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Sorry, but the answer is 20.

 Feb 12, 2021
 #3
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We know all factorials 10 and afterwards end in 00 (as there are two factors of 5 and enough factors of 2s), so it is really 5! which counts. This ends in 20, so the last two digits of the described following sum is clearly 20.

 

Answer:20

 

-CitrusCornflakes :)

 Feb 13, 2021

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