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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        The value of\[{{2}^{1/4}}{{.4}^{1/8}}{{.8}^{1/6}}....\infty \]is:

    A)  1                                            

    B)  2

    C)  3/2                                       

    D)  4

    Correct Answer: B

    Solution :

                    \[{{2}^{1/4}}{{.4}^{1/8}}{{.8}^{1/6}}.....\infty \] \[={{2}^{\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+.....\infty }}\]                 \[=\frac{1}{{{2}^{2}}}\left\{ \frac{1}{1-1/2}+\frac{1-1/2}{{{\left( 1-\frac{1}{2} \right)}^{2}}} \right\}\]                 \[={{2}^{1/{{2}^{2}}|2+2|}}={{2}^{1}}=2\]


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