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

  • question_answer
    The product (32)(32) 1/6(32)1/36 ...... to \[\infty \] is  [Kerala (Engg.) 2005]

    A) 16

    B)   32

    C) 64

    D) 0

    E) 62

    Correct Answer: C

    Solution :

    (32)(32)1/6(32)1/36......\[\infty \]= \[{{(32)}^{1+\frac{1}{6}+\frac{1}{36}+.....\infty }}\] \[={{(32)}^{\frac{1}{1-(1/6)}}}\]\[={{(32)}^{\frac{1}{5/6}}}={{(32)}^{6/5}}\]\[={{2}^{6}}=64\].


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