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1969 Canada National Olympiad
6
Classic factorial sum (posted before?)
Classic factorial sum (posted before?)
Source:
May 14, 2006
factorial
induction
Problem Statement
Find the sum of
1
⋅
1
!
+
2
⋅
2
!
+
3
⋅
3
!
+
⋯
+
(
n
−
1
)
(
n
−
1
)
!
+
n
⋅
n
!
1\cdot 1!+2\cdot 2!+3\cdot 3!+\cdots+(n-1)(n-1)!+n\cdot n!
1
⋅
1
!
+
2
⋅
2
!
+
3
⋅
3
!
+
⋯
+
(
n
−
1
)
(
n
−
1
)!
+
n
⋅
n
!
, where
n
!
=
n
(
n
−
1
)
(
n
−
2
)
⋯
2
⋅
1
n!=n(n-1)(n-2)\cdots2\cdot1
n
!
=
n
(
n
−
1
)
(
n
−
2
)
⋯
2
⋅
1
.
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