JEE Main & Advanced Mathematics Sequence & Series Question Bank Geometric Progression

  • question_answer
    If \[y=x+{{x}^{2}}+{{x}^{3}}+.......\,\infty ,\,\text{then}\,\,x=\] [DCE 1999]

    A) \[\frac{y}{1+y}\]

    B) \[\frac{1-y}{y}\]

    C) \[\frac{y}{1-y}\]

    D) None of these

    Correct Answer: A

    Solution :

    \[y=\frac{x}{1-x}\](Infinite G.P.) \[\therefore y-yx=x\] or \[y=x\,(1+y)\]i.e., \[x=\frac{y}{1+y}\].


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