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The double factorial, denoted by n!!, returns the product of all of the odd integers that are less than or equal to n. For example, 7!! = 7 times 5 times 3 times 1. What is the units digit of 1!! + 3!! + 5!! + 7!! + ... + 49!!?

 Nov 19, 2018
 #1
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deleted

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 Nov 19, 2018
edited by Rom  Nov 20, 2018
 #4
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You made a quick mistake forgetting the 1, but I caught it. Thank you for leading me in the right direction. :)

MathCuber  Nov 21, 2018
 #2
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Here are two different sums done on two different computers and they both agree!!
∑[(2n + 1)!!, n, 0, 24]=59654360733417426078066607239049

a=listfor(n, 0, 24,(2*n+1)!!;sum(a)=59 6543607334 1742607806 6607239049

Rom: You have a mistake somewhere!! Here is another way: (49 - 5) / 2 + 1= 23 x 5=115+3!!+1!! =119.

Also: ∑[(2n+1)!!, n, 0, 24] mod 10 = 9!

 Nov 19, 2018
edited by Guest  Nov 19, 2018
edited by Guest  Nov 19, 2018
 #3
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As Rom points out....5!!   + 7!!   +  9!!   +  .....+  49!!    will end in 5

 

[ Each term  will have 5 * an odd product ...i.e., ending in a "5"....and we will have 23 terms....so....an odd number of summed  terms ending in "5" will also end in "5"  ]

 

And   

 

1!!   = 1

3!! = 3

 

So....the sum ends in   1 + 3   + 5   =    9

 

 

 

 

cool cool cool

 Nov 19, 2018
edited by CPhill  Nov 20, 2018

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