The-Value-of-the-sum-n-1-13-i-n-i-n-1-Where-i-1-is-a-i-b-i-1-c-i-d-0-

Question Number 16374 by gourav~ last updated on 21/Jun/17

T h e V a l u e o f t h e s u m . . \underset{n = 1}{\sum^{13}} (i^{n} + i^{n + 1}), W h e r e i = \sqrt{- 1}

i s . .

(a .) i

(b .) i - 1

(c .) - i

(d .) 0

Answered by Tinkutara last updated on 21/Jun/17

(i^{1} + i^{2}) + (i^{2} + i^{3}) + (i^{3} + i^{4}) + \dots +

(i^{12} + i^{13}) + (i^{13} + i^{14})

= (i^{1} + i^{14}) + 2 (i^{2} + i^{3} + \dots + i^{13})

= i + (- 1) = i - 1

(Using the general rule :

i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3} = 0)