Question

If $i^2=-1,$ then the sum $i+i^2+i^3+...$ upto 1000 terms is equal to:

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

Answer 1

Answer: (E)

$i+i^2+i^3+...$ upto 1000 terms $=\frac{i(1-i^{1000})}{1-i}=\frac{i(1-1)}{1-i}$ $=\frac{i}{1-i}\times 0=0$