2. Solved Papers
  3. BCECE Engineering

BCECE Engineering BCECE Engineering Solved Paper-2011

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

    A)  \[i\]                                       

    B)         \[i-1\]                   

    C)         \[-i\]                                      

    D)         0

    Correct Answer: B

    Solution :

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


You need to login to perform this action.
You will be redirected in 3 sec spinner