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What is the sum of 'n' terms in the series: $\log m + \log \frac{m^2}{n} + \log \frac{m^3}{n^2} + \log \frac{m^4}{n^3} + \dots + \log \frac{m^n}{n^{n-1}}?$

1. $\log \left[\frac{n^{n-1}}{m^{(n+1)}} \right]^{\frac{n}{2}}$
2. $\log \left[\frac{m^m}{n^n} \right]^{\frac{n}{2}}$
3. $\log \left[\frac{m^{(1-n)}}{n^{(1-m)}} \right]^{\frac{n}{2}}$
4. $\log \left[\frac{m^{(n+1)}}{n^{(n-1)}} \right]^{\frac{n}{2}}$

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