Yes, thank you for pointing that out. We should compare that sequence to just 1/(2^n), but thankfully that does not change the final answer. Now keep in mind not every term in the sequence is positive though because take for example cos( π/2 + kπ) for any integer k. That would result in the term being 0 and 0 is obviously not positive. I apologize for any confusion.
For problem no 5, how can cos^2 (x) be between -1 and 1, shouldn't it be always positive because of the even power?
Yes, thank you for pointing that out. We should compare that sequence to just 1/(2^n), but thankfully that does not change the final answer. Now keep in mind not every term in the sequence is positive though because take for example cos( π/2 + kπ) for any integer k. That would result in the term being 0 and 0 is obviously not positive. I apologize for any confusion.
@@thecalculusgod thank you for confirming, I tripped a bit. it didn't change the outcome anyways as you said!