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. 0

Answer 1

The correct option is D

0

$i+i^2+i^3+....i^{1000}i+i^2+i^3+i^4{i}^{1000}[\because i^2=-1,i^3=-i,i^4=1]=i-1-i+1=0$

Similarly, the sum of the next four terms of the series will be equal to 0. This is because the powers of i follow a cyclicity of 4. Hence, the sum of all terms, till 1000, will be zero.

$i+i^2+i^3+.....i^{1000}=0$