Does the sequence $\displaystyle c_n= \frac {sin(n) +2log(n)} {cos(n) + log(n)}$ converge? Any hints? Do I use L'Hopital, the squeeze rule?
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First show that $\displaystyle \frac{2\ln(n)-1}{\ln(n)-1}\le c_n \le\frac{1+2\ln(n)}{1+\ln(n)}$, then use L'Hopital.
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