Question 72
For every positive integer $n$ let $f(n)$ be the product of all odd natural numbers less than or equal to $2n+1$ (for example $f(4)=1 \cdot 3 \cdot 5 \cdot 7 \cdot 9$). Let then $g(n)=\frac{n}{f(n)}$. What can be said about the sum $S=g(1)+g(2)+\cdots+g(30)$?
(A) $S \leq 0.35$
(B) $0.35\lt S \leq 0.49$
(C) $0.49\lt S \leq 0.50$
(D) $0.50\lt S \leq 0.51$
(E) $S\gt 0.51$
(A) $S \leq 0.35$
(B) $0.35\lt S \leq 0.49$
(C) $0.49\lt S \leq 0.50$
(D) $0.50\lt S \leq 0.51$
(E) $S\gt 0.51$