Question

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

• A. $i$
• B. $i-1$
• C. $1$
• D. $0$

Answer 1

The correct option is B $i-1$

$\sum _{n=1}^{13}(i^n+i^{n+1})=(i+i^2)+(i^2+i^3)+.....+(i^{13}+i^{14})$
By putting the value of $i^2=-1$ we get
$\sum _{n=1}^{13}(i^n+i^{i+1})=i-1$