SOLUTION: Find the limits of the sequences. an= cos(n*pi /2) Thank you so much!

Algebra ->  Sequences-and-series -> SOLUTION: Find the limits of the sequences. an= cos(n*pi /2) Thank you so much!      Log On


   

Question 579911: Find the limits of the sequences.
an= cos(n*pi /2)
Thank you so much!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D=+cos%28pi%2F2%29=0, a%5B2%5D=+cos%282%2Api%2F2%29=cos%28pi%29=-1, a%5B3%5D=+cos%283%2Api%2F2%29+=0, a%5B4%5D=+cos%284%2Api%2F2%29=cos%282%2Api%29=1, and it repeats from then on because cosine is periodic with a period of 2%2Api, so a%5B5%5D=a%5B1%5D=0, a%5B6%5D=a%5B2%5D=-1 and so on. In general a%5Bn%2B4%5D=a%5Bn%5D
-1%3Ca%5Bn%5D=cos%28n%2Api%2F2%29+%3C=1, but a%5Bn%5D does not converge. It just keeps flip-flopping between 1 and -1, hitting 0 in between. There is no limit.