2
$\begingroup$

Here is the sequence:

$$a_n = \frac{n^2}{cn^2 + 1} \mbox{ where } c < 0.$$

If I prove this function has a limit using the limit definition, as $n$ goes to infinity, does that prove the sequence converges?

  • 0
    One would expect. Of course, you should have a candidate L in mind for the value of the limit. Then all you need to do is show that $a_{n} - L$ can be made arbitrarily small in absolute value by choosing $n$ large enough.2011-10-24

1 Answers 1