JEE Main & Advanced Mathematics Other Series Question Bank Critical Thinking

  • question_answer 7) If  \[S=\sum\limits_{n=0}^{\infty }{\frac{{{(\log x)}^{2n}}}{(2n)\,!},}\] then \[S\] =

    A) \[x+{{x}^{-1}}\]

    B) \[x-{{x}^{-1}}\]

    C) \[\frac{1}{2}(x+{{x}^{-1}})\]

    D) None of these

    Correct Answer: C

    Solution :

    We have \[S=\sum\limits_{n=0}^{\infty }{\frac{{{(\log x)}^{2n}}}{(2n)!}=\left( \frac{{{e}^{\log x}}+{{e}^{-\log x}}}{2} \right)}=\frac{x+{{x}^{-1}}}{2}\].

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