Question

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

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

Answer 1

The correct option is B $i-1$

$\sum (i^n+i^{n+1})=i+2(i^2+i^3+i^4.........i^{13})+i^{14}$

$=i+2\left(0\right)-1$.........................($i^2=-1,i^3=-i,i^4=1$)

$=i-1$