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Math Prize For Girls Problems
2016 Math Prize for Girls Problems
6
6
Part of
2016 Math Prize for Girls Problems
Problems
(1)
Math Prize 2016 Problem 6
Source:
9/12/2016
The largest term in the binomial expansion of
(
1
+
1
2
)
31
(1 + \tfrac{1}{2})^{31}
(
1
+
2
1
)
31
is of the form
a
b
\frac{a}{b}
b
a
, where
a
a
a
and
b
b
b
are relatively prime positive integers. What is the value of
b
b
b
? As an example of a binomial expansion, the binomial expansion of an expression of the form
(
x
+
y
)
3
(x + y)^3
(
x
+
y
)
3
is the sum of four terms
x
3
+
3
x
2
y
+
3
x
y
2
+
y
3
.
x^3 + 3x^2y + 3xy^2 + y^3.
x
3
+
3
x
2
y
+
3
x
y
2
+
y
3
.
Math Prize for Girls