Q. 7

# Mark the Correct alternative in the following:If i2 = - 1, then the sum i + i2 + i3 + …. upto 1000 terms is equal toA. 1B. -1C. iD. 0

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 4th terms. So, there are total 250 pairs are made and each pair have value equal to 0.

S = 0

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Evaluate:

(i) (iii) .

RS Aggarwal - Mathematics