Question

{\displaystyle \lim _{n\to \infty }{\frac {1}{n}}=0}{\displaystyle \lim _{n\to \infty }{\frac {1}{n}}=0}

Answer 1

The limit is true and it exists

Explanation:

Given the limit
`{\displaystyle \lim _(n\to \infty ){\frac {1}{n}}=0}`

To show that the given limit is true, we will simply replace n with ∞

On substituting

`{\displaystyle \lim _(n\to \infty ){\frac {1}{n}}=0}\\ = (1)/(\infty)\\= 0\\`

Hence the given limit is true and it exists since we got a finite value. Note that for any constant a, lim n ->∞ a/n = 0