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JCECE Engineering JCECE Engineering Solved Paper-2008

  • question_answer
    The value of\[1-\log 2+\frac{{{(\log 2)}^{2}}}{2!}-\frac{{{(\log )}^{3}}}{3!}+...\]is

    A) \[\log 3\]                                            

    B) \[\log 2\]

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

    D)  None of these

    Correct Answer: C

    Solution :

    Key Idea In a given series there is a factorial in denominator, therefore it may be in the form of exponential series. \[\therefore \]  \[1-\log 2+\frac{{{(\log 2)}^{2}}}{2!}-\frac{{{(\log 2)}^{3}}}{3!}+...\]                 \[={{e}^{-\log 2}}\]                 \[={{e}^{\log {{2}^{-1}}}}\]                 \[={{2}^{-1}}=\frac{1}{2}\]


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