+537 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!!?
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!
+128406 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
