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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 45

  • question_answer
    \[K=\underset{x\to \infty }{\mathop{\lim }}\,\left[ \frac{\sum\limits_{K=1}^{1000}{{{(x+k)}^{m}}}}{{{X}^{m}}+{{10}^{1000}}} \right](m>101)\]is-

    A) 10                    

    B)        \[{{10}^{2}}\]

    C) \[{{10}^{3}}\]             

    D)        \[{{10}^{4}}\]

    Correct Answer: C

    Solution :

    [c] \[K=\underset{x\to \infty }{\mathop{\lim }}\,\left[ \frac{{{X}^{m}}\sum\limits_{k=1}^{1000}{{{\left( 1+\frac{k}{x} \right)}^{m}}}}{{{x}^{m}}\left( 1+\frac{{{10}^{1000}}}{{{x}^{m}}} \right)} \right]\] \[=\frac{1+1+....+1}{1}=1000\]


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