Is there a relatively fast way of solving this?
If which of the following statements are true?
Thanks for your help!
songoku's method is the fastest. You need to recognize the fact that the powers of i cycle through four different numbers: 1, i, -1, and -i. The sum of any four consecutive powers of i will be 0. The fraction could be written like this:
The sum of the first four powers of i shown above is
So how many powers of i are being added all together? What is the sum in the numerator? If you can answer these questions, you'll know what the fraction simplifies to.