Question

$i^2+i^4+i^6+..........(2n+1)$terms equal to:

• A. $i$
• B. $-i$
• C. $1$
• D. $-1$

Answer 1

The correct option is D

$-1$

Evaluating the given series.

$$\begin{gathered} \Rightarrow i^2+i^4+i^6+......(2n+1)terms \\ =i^2+i^4+i^6+...\text{upto some odd number of terms} \\ =-1+1-1+...\text{upto odd number terms}\left[Thelasttermwillhavereducedpower=2\right] \\ =-1 \end{gathered}$$

Hence, the correct answer is Option (D).