Question

How do you determine whether the sequence `a_n=(n+2)/n` converges, if so how do you find the limit?

Answer 1

It coverages to unity..

Explanation:

We have the sequence `{a_n}` where:

`a_n = (n+2)/n`
`\ \ \ \ = 1+2/n`

And so as `n rarr oo => a_n rarr 1`

NB: A common result is that the harmonic series `sum_(r=1)^oo 1/r` diverges and hence the series `sum_(r=1)^oo a_r` diverges.

We can also visualise how the sequence behaves by looking at the graph of the function:

graph{(x+2)/x [-10, 10, -5, 5]}