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7
Factorials Reciprocals
Factorials Reciprocals
Source:
December 9, 2005
factorial
floor function
Problem Statement
Given that
1
2
!
17
!
+
1
3
!
16
!
+
1
4
!
15
!
+
1
5
!
14
!
+
1
6
!
13
!
+
1
7
!
12
!
+
1
8
!
11
!
+
1
9
!
10
!
=
N
1
!
18
!
\frac 1{2!17!}+\frac 1{3!16!}+\frac 1{4!15!}+\frac 1{5!14!}+\frac 1{6!13!}+\frac 1{7!12!}+\frac 1{8!11!}+\frac 1{9!10!}=\frac N{1!18!}
2
!
17
!
1
+
3
!
16
!
1
+
4
!
15
!
1
+
5
!
14
!
1
+
6
!
13
!
1
+
7
!
12
!
1
+
8
!
11
!
1
+
9
!
10
!
1
=
1
!
18
!
N
find the greatest integer that is less than
N
100
.
\frac N{100}.
100
N
.
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