Summation of factorials
n
=
1
∑
1
0
0
(
n
!
m
o
d
1
0
0
)
=
?
The answer is 213.
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1 solution
Moderator note:
It's better to clarify why you stopped at n = 9 .
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From n = 1 0 onwards, n ! can be factorized with 2 × 5 × 2 × 5 . Therefore, any number greater than 10 would yield a remainder of z e r o
So, we need only calculate the factorials of numbers uptil 9, the rest will not affect the final value.
Which are respectively, 1 , 2 , 6 , 2 4 , 1 2 0 , 7 2 0 , 5 0 4 0 , 4 0 3 2 0 , 3 6 2 8 8 0 .Which, with modulo 1 0 0 yields 1 , 2 , 6 , 2 4 , 2 0 , 2 0 , 4 0 , 2 0 , 8 0
have a value until n=9 , then equal "zero"
So (1+2+6+24+20+20+40+20+80)=213