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Mathematics
Problem
Let
G
1
,
G
2
,
…
,
G
k
G_1,G_2,\dots,G_k
G
1
,
G
2
,
…
,
G
k
be
k
k
k
geometric means inserted between two positive numbers
a
a
a
and
b
b
b
. Which of the following equals the product
G
1
G
2
…
G
k
G_1G_2\dots G_k
G
1
G
2
…
G
k
? a)
(
a
b
)
k
+
2
2
(ab)^{\frac{k+2}{2}}
(
ab
)
2
k
+
2
b)
a
k
−
1
2
b
k
+
1
2
a^{\frac{k-1}{2}}\,b^{\frac{k+1}{2}}
a
2
k
−
1
b
2
k
+
1
c)
(
a
b
)
k
/
2
(ab)^{k/2}
(
ab
)
k
/2
d)
(
a
+
b
)
k
(a+b)^k
(
a
+
b
)
k
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