CAT Quant Practice Problems

Question: Let S denotes the infinite sum \(2 + 5x + 9{x^2} + 14{x^3} + 20{x^4} + ...,\)where \(\left| x \right| < 1\)and the coefficient of \(x^{n-1} is \frac{1}{2}n(n + 3),(n = 1,{\rm{ }}2,{\rm{ }}...).\)Then S equals:
  1. \(\frac{{2 - x}}{{{{\left( {1 - x} \right)}^{3\,}}}}\)
  2. \(\frac{{2 - x}}{{{{\left( {1 + x} \right)}^{3\,}}}}\)
  3. \(\frac{{2 + x}}{{{{\left( {1 - x} \right)}^{3\,}}}}\)
  4. \(\frac{{2 - x}}{{{{\left( {1 + x} \right)}^{3\,}}}}\)

Correct Option:1

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