Question

does cos^(2)n/(2^n) converge?

Answer 1

are you asking if \(\displaystyle \lim_{n\to\infty}\frac{\cos^2(n)}{2^n}\) converges?

Answer 2

It does

Answer 3

how did you come to that conclusion? Can you show me the math?

Answer 4

\[-1 \leq\cos^2(n) \leq 1\]
\[\frac{-1}{2^n} \leq\frac{\cos^2(n)}{2^n}\leq\frac{1}{2^n}\]
evaluating both the limits as n goes to infinity of -1/2^n and 1/2^n gives us 0 for both\[0\leq\lim_{n\rightarrow \infty} \frac{\cos^2(n)}{2^n} \leq 0\]applying the squeeze theorem here will show you that the sequence converges.

Answer 5

thanks!