Question

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

• A. I
• B. i – 1
• C. –I
• D. 0

Answer 1

Answer: (B)

i – 1

Answer 2

Sol.

$\sum_{n = 1}^{13}i^{n}$+ $\sum_{n = 1}^{13}i^{n + 1}$

= (i + i² + ..... i¹³) + (i² + i³ + ....... i¹⁴)

= (i + 0) + (i² + 0)

= i – 1