MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Math Prize For Girls Problems
2014 Math Prize For Girls Problems
7
Math Prize 2014 Problem 7
Math Prize 2014 Problem 7
Source:
September 29, 2014
Problem Statement
If
x
x
x
is a real number and
k
k
k
is a nonnegative integer, recall that the binomial coefficient
(
x
k
)
\binom{x}{k}
(
k
x
)
is defined by the formula
(
x
k
)
=
x
(
x
−
1
)
(
x
−
2
)
…
(
x
−
k
+
1
)
k
!
.
\binom{x}{k} = \frac{x(x - 1)(x - 2) \dots (x - k + 1)}{k!} \, .
(
k
x
)
=
k
!
x
(
x
−
1
)
(
x
−
2
)
…
(
x
−
k
+
1
)
.
Compute the value of
(
1
/
2
2014
)
⋅
4
2014
(
4028
2014
)
.
\frac{\binom{1/2}{2014} \cdot 4^{2014}}{\binom{4028}{2014}} \, .
(
2014
4028
)
(
2014
1/2
)
⋅
4
2014
.
Back to Problems
View on AoPS