Question

The value of ${\sum }_{n=1}^{13}(i^n+i^{n+1})$, where $i=\sqrt{-1}$

• A. $i$
• B. $i-1$
• C. $-1$
• D. $0$

Answer 1

The correct option is B $i-1$

$\sum _{n=1}^{13}(i^n+i^{n+1})$ where $i=\sqrt{-1}$

$\Rightarrow (i+i^2)+(i^2+i^3)+(i^3+i^4)+.....+\left(i^{1/2}{i}^{1/3}\right)+(i^{1/3}+i^{1/4})$

$\Rightarrow (i-1)+(-1-i)+(-i+1)+.....+(1+i)+(i-1)$

$=i-1$.