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JEE Main & Advanced Sample Paper JEE Main Sample Paper-23

  • question_answer
    Let \[{{S}_{n}}={{n}^{-2015}}(1+{{2}^{2014}}+{{3}^{2014}}+......+{{n}^{-2014}})\], then \[\underset{n\to \infty }{\mathop{\lim }}\,{{S}_{n}}\] is

    A)  1                                

    B)  \[\frac{1}{2014}\]

    C)  \[\frac{1}{2015}\]                                

    D)  \[\frac{2014}{2015}\]

    Correct Answer: C

    Solution :

    \[{{S}_{n}}\,=\sum\limits_{i=1}^{n}{\frac{1}{n}{{\left( \frac{1}{n} \right)}^{2014}}\,=\int\limits_{0}^{1}{{{x}^{2014}}dx=\frac{1}{2015}}}\]


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