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ISI B.Math Entrance Exam
2006 ISI B.Math Entrance Exam
3
B.Math - equation
B.Math - equation
Source:
June 17, 2012
induction
algebra proposed
algebra
Problem Statement
Find all roots of the equation :-
1
−
x
1
+
x
(
x
−
1
)
2
!
−
⋯
+
(
−
1
)
n
x
(
x
−
1
)
(
x
−
2
)
.
.
.
(
x
−
n
+
1
)
n
!
=
0
1-\frac{x}{1}+\frac{x(x-1)}{2!} - \cdots +(-1)^n\frac{x(x-1)(x-2)...(x-n+1)}{n!}=0
1
−
1
x
+
2
!
x
(
x
−
1
)
−
⋯
+
(
−
1
)
n
n
!
x
(
x
−
1
)
(
x
−
2
)
...
(
x
−
n
+
1
)
=
0
.
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