10th Class Mathematics Related to Competitive Exam Question Bank Algebra

  • question_answer
    The sum of the series\[1+{{\log }_{e}}2+\frac{{{({{\log }_{e}}2)}^{2}}}{2!}+\frac{{{({{\log }_{e}}2)}^{2}}}{3!}+.....\,\,\,to\,\,\infty \] is

    A)  2                              

    B)         1

    C)  0                            

    D)         -

    Correct Answer: A

    Solution :

     Sum\[=1+{{\log }_{e}}2+\frac{{{({{\log }_{e}}2)}^{2}}}{\left| \!{\nderline {\,   2 \,}} \right. }+\frac{{{({{\log }_{e}}2)}^{3}}}{\left| \!{\nderline {\,   3 \,}} \right. }+...\infty \]             \[={{e}^{{{\log }_{e}}^{2}}}=2\]


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