A) i
B) i - 1
C) - i
D) 0
Correct Answer: B
Solution :
[b]: \[\sum\limits_{n=1}^{13}{({{i}^{n}}+{{i}^{n+1}})}=\sum\limits_{n=1}^{13}{{{i}^{n}}}(1+i)=(1+i)\sum\limits_{n=1}^{13}{{{i}^{n}}}\] \[=(1+i)(i+{{i}^{2}}+{{i}^{3}}+...+{{i}^{13}})\] \[=(1+i)\left\{ \frac{i(1-{{i}^{13}})}{1-i} \right\}=(1+i)i=-1+i\]You need to login to perform this action.
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