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For all positive integers \(n\) and \(m,\) the function \(A(n)\) equals the following product:
\(\left(1 + \dfrac12 + \dfrac1{2^2}\right)\left(1 + \dfrac13 + \dfrac1{3^2}\right)\left(1 +\dfrac15 + \dfrac1{5^2}\right)\cdots\left(1 + \dfrac1{p_n} + \dfrac1{p_n^2}\right),\) where \(p_n\) is the \(nth\) smallest prime number, while \(B(m)\) equals the sum of the reciprocals of all the positive integers from \(1\) through \(m,\) inclusive. The largest reciprocal of an integer in the sum that \(B(25)\) represents that is NOT present in the distributed expansion of \(A(5)\) is
A. \(\dfrac14\)
B. \(\dfrac15\)
C. \(\dfrac16\)
D. \(\dfrac17\)
E. \(\dfrac18\)
Answer: E
Source: Manhattan GMAT
\(\left(1 + \dfrac12 + \dfrac1{2^2}\right)\left(1 + \dfrac13 + \dfrac1{3^2}\right)\left(1 +\dfrac15 + \dfrac1{5^2}\right)\cdots\left(1 + \dfrac1{p_n} + \dfrac1{p_n^2}\right),\) where \(p_n\) is the \(nth\) smallest prime number, while \(B(m)\) equals the sum of the reciprocals of all the positive integers from \(1\) through \(m,\) inclusive. The largest reciprocal of an integer in the sum that \(B(25)\) represents that is NOT present in the distributed expansion of \(A(5)\) is
A. \(\dfrac14\)
B. \(\dfrac15\)
C. \(\dfrac16\)
D. \(\dfrac17\)
E. \(\dfrac18\)
Answer: E
Source: Manhattan GMAT
