So Complex

Algebra Level 2

What is the value of ∑ r = 1 100 i r \sum _{ r=1 }^{ 100 }{ { i }^{ r } } . (Here i stands for iota)

0 -1 1 -i

Aman Baser by Aman Baser , 21, India

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2 solutions

Abhinandan Padhi
Jun 14, 2015

Every 4 terms, the sum becomes i + (-1) + (-i) + 1. The sum of these is 0. Hence, at the 100th term, the sum is also zero.

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Shravan Kumar
Aug 23, 2015

Substitute i with -1 then you get a series of 1 and -1 which results in 0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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