Question

If i² = - 1, then the sum i + i² + i³ + …. upto 1000 terms is equal to 

A. 1 

B. -1 

C. i 

D. 0

Answer 1

We know that

 i⁴ⁿ⁺¹ = i 

i⁴ⁿ⁺² = i² = -1

i⁴ⁿ⁺³ = i³ = -i

i⁴ⁿ⁺⁴ = i⁴ = 1 

i⁴ⁿ⁺¹ + i⁴ⁿ⁺² + i⁴ⁿ⁺³ + i⁴ⁿ⁺⁴ = i + (-1) + (-i) + 1 

= 0 

S = i + i² + i³ + …… upto 1000 terms 

We can make the pair of 4 terms because we know that value is repeat after every 4^th terms. So, there are total 250 pairs are made and each pair have value equal to 0. 

S = 0