Question

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

• A. i
• B. i-1
• C. -i
• D. 0

Answer 1

The correct option is B

i-1

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

= $\frac{i(1-i^{13})}{1-i}+\frac{i^2(1-i^{13})}{1-i}$

= i$\left(\frac{1-i}{1-i}\right)+\frac{i^2(1-i)}{(1-i)}=i+i^2=i-1$ .