If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then Sis between which of the following two fractions?
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A\frac{1}{3} and \frac{1}{2}
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B\frac{1}{4} and \frac{1}{3}
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C\frac{1}{5} and \frac{1}{4}
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D\frac{1}{6} and \frac{1}{5}
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E\frac{1}{7} and \frac{1}{6}