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

  • question_answer
    If the sum of the series \[1+\frac{2}{x}+\frac{4}{{{x}^{2}}}+\frac{8}{{{x}^{3}}}+....\infty \] is a  finite number, then [UPSEAT 2002]

    A) \[x>2\]

    B) \[x>-2\]

    C) \[x>\frac{1}{2}\]

    D) None of these

    Correct Answer: A

    Solution :

    Common ratio \[(r)=\frac{2}{x}\] For sum to be finite \[r<1\] \[\Rightarrow \]\[\frac{2}{x}<1\] \[\Rightarrow \]\[2<x\] \[\Rightarrow \]\[x>2\].


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