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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

  • question_answer
        \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}{{e}^{r/n}}}\]is

    A)  \[e\]                                    

    B)  \[e-1\]

    C)  \[1-e\]                                

    D)  \[e+1\]

    Correct Answer: B

    Solution :

                    Now,     \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}}\,\,{{e}^{r/n}}\] \[=\int_{0}^{1}{{{e}^{x}}}dx=[{{e}^{x}}]_{0}^{1}\] \[=e-1\]              


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