Imaginary unit/Introductory
- Find the sum of .
- Find the product of .
Contents
[hide]Solution 1
Since repeats in a n exponential series at every fifth turn, the sequence repeats. Note that this sums to . That means that all sequences have a sum of zero (k is a natural number). Since , the original series sums to the first two terms of the powers of i, which equals .
Solution 2
, so the product is equal to .