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JCECE Engineering JCECE Engineering Solved Paper-2003

  • question_answer
    \[(1+3){{\log }_{e}}3+\frac{1+{{3}^{2}}}{2!}{{({{\log }_{e}}3)}^{2}}\]\[+\frac{1+{{3}^{3}}}{3!}{{({{\log }_{e}}3)}^{3}}+...\infty \]is equal to:

    A) \[28\]                                   

    B) \[30\]

    C) \[25\]                                   

    D) \[0\]

    Correct Answer: A

    Solution :

    Let\[S=(1+3){{\log }_{e}}3+\frac{1+{{3}^{2}}}{2!}{{({{\log }_{e}}3)}^{2}}+...\]                 \[S=\left( {{\log }_{e}}3+\frac{1}{2!}{{({{\log }_{e}}3)}^{2}}+... \right)\]                 \[=({{e}^{{{\log }_{e}}3}}-1)+({{e}^{3{{\log }_{e}}3}}-1)\]                 \[=(3-1)+(27-1)\]                 \[=28\]


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