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1953 Moscow Mathematical Olympiad
256
MMO 256 Moscow MO 1953 solve sum (-1)^nx(x-1)...(x - n + 1)}{n!}=0
MMO 256 Moscow MO 1953 solve sum (-1)^nx(x-1)...(x - n + 1)}{n!}=0
Source:
August 9, 2019
equation
factorial
algebra
Problem Statement
Find roots of the equation
1
−
x
1
+
x
(
x
−
1
)
2
!
−
.
.
.
+
(
−
1
)
n
x
(
x
−
1
)
.
.
.
(
x
−
n
+
1
)
n
!
=
0
1 -\frac{x}{1}+ \frac{x(x - 1)}{2!} -... +\frac{ (-1)^nx(x-1)...(x - n + 1)}{n!}= 0
1
−
1
x
+
2
!
x
(
x
−
1
)
−
...
+
n
!
(
−
1
)
n
x
(
x
−
1
)
...
(
x
−
n
+
1
)
=
0
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