JEE Main & Advanced Mathematics Sequence & Series Question Bank Exponential series

  • question_answer
    \[\frac{2}{1\,!}{{\log }_{e}}2+\frac{{{2}^{2}}}{2\,!}{{({{\log }_{e}}2)}^{2}}+\frac{{{2}^{3}}}{3\,!}{{({{\log }_{e}}2)}^{3}}+.....\infty =\]

    A) 2

    B) 3

    C) 4

    D) None of these

    Correct Answer: B

    Solution :

    Sum =\[({{e}^{2{{\log }_{e}}2}}-1)=4-1=3\].


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