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Successive odd integers divided by 7

Source: 1976 AHSME Problem 21

May 19, 2014
AMC

Problem Statement

What is the smallest positive odd integer nn such that the product 21/723/7⋯2(2n+1)/72^{1/7}2^{3/7}\cdots2^{(2n+1)/7} is greater than 10001000? (In the product the denominators of the exponents are all sevens, and the numerators are the successive odd integers from 11 to 2n+12n+1.)
<spanclass=′latex−bold′>(A)</span>7<spanclass=′latex−bold′>(B)</span>9<spanclass=′latex−bold′>(C)</span>11<spanclass=′latex−bold′>(D)</span>17<spanclass=′latex−bold′>(E)</span>19<span class='latex-bold'>(A) </span>7\qquad<span class='latex-bold'>(B) </span>9\qquad<span class='latex-bold'>(C) </span>11\qquad<span class='latex-bold'>(D) </span>17\qquad <span class='latex-bold'>(E) </span>19
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