Question

Check whether or not the sequence (n- 1/n) is convergent

Answer 1

$$\lim\limits_{n\to \infin}a_n=\lim\limits_{n\to \infin}(n-\dfrac{1}{n})$$

$$=\lim\limits_{n\to \infin}n-\lim\limits_{n\to \infin}\dfrac{1}{n}=\lim\limits_{n\to \infin}n-0=\infin$$

The sequence $(n-\dfrac{1}{n})$ is not convergent.