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Problem
Problem
If
f
(
n
)
=
∏
i
=
2
n
−
1
log
i
(
i
+
1
)
f(n) = \prod_{i=2}^{n-1} \log_i(i+1)
f
(
n
)
=
∏
i
=
2
n
−
1
lo
g
i
(
i
+
1
)
, the value of
∑
k
=
1
100
f
(
2
k
)
\sum_{k=1}^{100} f(2^k)
∑
k
=
1
100
f
(
2
k
)
equals a. 5010 b. 5050 c. 5100 d. 5049
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