prove that sequence $cos~(1/n)$ is converging to 1. using the definition. ie, I want to find the $N$ corresponding to the $\epsilon$ in definition. I am stuck with, whether i can use $cos^{-1}$ in both sides of inequality without altering sign of inequality.
2026-03-25 22:03:27.1774476207
prove convergence of the sequence cos(1/n) using formal definition
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$\cos (\frac 1 n) \geq 1-\frac 1 {n^{2}}$ so $|1-\cos (\frac 1 n)| <\epsilon$ if $n>\frac 1 {\sqrt{\epsilon}}$