CAT Quant Practice Problems

Question: What is the sum of ‘n’ terms in the series\(\log m + \log \left( {\frac{{{m^2}}}{n}} \right) + \log \left( {\frac{{{m^2}}}{{{n^2}}}} \right) + \log \left( {\frac{{{m^4}}}{{{n^3}}}} \right)...?\)
  1. \(\log {\left[ {\frac{{n\left( {n - 1} \right)}}{{m\left( {n + 1} \right)}}} \right]^{\frac{n}{2}}}\)
  2. \(\log {\left[ {\frac{{{m^m}}}{{{n^n}}}} \right]^{\frac{n}{2}}}\)
  3. \(\log {\left[ {\frac{{{m^{\left( {1 - n} \right)}}}}{{{n^{\left( {1 - m} \right)}}}}} \right]^{\frac{n}{2}}}\)
  4. \(\log {\left[ {\frac{{{m^{\left( {n + 1} \right)}}}}{{{n^{\left( {n - 1} \right)}}}}} \right]^{\frac{n}{2}}}\)

Correct Option:4

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