- Thread starter
- #1

- Jan 29, 2012

- 661

Here is a link to the question:an= (e^2n + 6n) ^1/2

Find the limit of sequence? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

- Thread starter Fernando Revilla
- Start date

- Thread starter
- #1

- Jan 29, 2012

- 661

Here is a link to the question:an= (e^2n + 6n) ^1/2

Find the limit of sequence? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

- Thread starter
- #2

- Jan 29, 2012

- 661

I suppose you meant $e^{2n}$, not $e^2n$. One way: we have $a_n=(e^{2n} + 6n) ^{1/2}>n^{1/2}$. Suppose $K>0$ then, $n^{1/2}>K\Leftrightarrow n>K^2$. Choosing $n_0=\lfloor K^2\rfloor+1$, if $n\ge n_0$ then $n^{1/2}>K$ and this means that $\displaystyle\lim_{n\to +\infty}n^{1/2}=+\infty$. As a consequence, $\displaystyle\lim_{n\to +\infty}a_n=+\infty$.

Alternatively, you can use well known properties of elementary functions and the