Please help!
Use the squeezing theorem to find the limit of the sequence
Hello,
First of all, you can divide the numerator & the denominator by n
--> $\displaystyle a_n=\frac{\sin(n)+3\cos(n)}{n+1}$
Now, the squeeze theorem.
(these are all $\displaystyle \leq$)
-1<sin(n)<1
-1<cos(n)<1 --> -3<3cos(n)<3
---> -1-3<sin(n)+3cos(n)<1+3
Hence, $\displaystyle \frac{-4}{n+1}<a_n=\frac{\sin(n)+3\cos(n)}{n+1}<\frac{4}{ n+1}$