If ~$S$~ is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then ~$S$~ is between which of the following two fractions?


~$\frac{1}{3}$~and~$\frac{1}{2}$~

~$\frac{1}{4}$~and~$\frac{1}{3}$~

~$\frac{1}{5}$~and~$\frac{1}{4}$~

~$\frac{1}{6}$~and~$\frac{1}{5}$~

~$\frac{1}{7}$~and~$\frac{1}{6}$~

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