Find the value of $\frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56}$.
Options:
- A: $\frac{3}{8}$
- B: $\frac{1}{4}$
- C: $\frac{2}{7}$
- D: $\frac{5}{12}$
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