Evaluate the sum of the series: $\log_e \frac{4}{5} + \frac{1}{4} - \frac{1}{2} \left( \frac{1}{4} \right)^2 + \frac{1}{3} \left( \frac{1}{4} \right)^3 - \dots$
- A$2 \log_e \frac{4}{5}$
- B$\log_e \frac{5}{4}$
- C$1$
- D$0$
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