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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 15

  • question_answer
    The value of \[sum\sum\limits_{n=1}^{13}{({{i}^{n}}+{{i}^{n+1}})}\], where\[i=\sqrt{-1}\] equals     

    A) i

    B) i - 1

    C) - i

    D)  0

    Correct Answer: B

    Solution :

    [b]: \[\sum\limits_{n=1}^{13}{({{i}^{n}}+{{i}^{n+1}})}=\sum\limits_{n=1}^{13}{{{i}^{n}}}(1+i)=(1+i)\sum\limits_{n=1}^{13}{{{i}^{n}}}\] \[=(1+i)(i+{{i}^{2}}+{{i}^{3}}+...+{{i}^{13}})\] \[=(1+i)\left\{ \frac{i(1-{{i}^{13}})}{1-i} \right\}=(1+i)i=-1+i\]


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