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JEE Main & Advanced AIEEE Solved Paper-2002

  • question_answer
    \[\sum\limits_{n=0}^{\infty }{\frac{{{({{\log }_{e}}x)}^{n}}}{n!}}\] is equal to   AIEEE  Solved  Paper-2002

    A)                                         \[{{\log }_{e}}x\] 

    B)                                           \[x\]         

    C)           \[{{\log }_{x}}e\]                

    D)           None of these

    Correct Answer: B

    Solution :

       \[\sum\limits_{n=0}^{\infty }{\frac{{{({{\log }_{e}}x)}^{n}}}{n!}=1+\frac{{{\log }_{e}}x}{1!}+\frac{{{({{\log }_{e}}x)}^{2}}}{2!}+...}\]                    \[={{e}^{{{\log }_{e}}x}}=x\]


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