Math Help - Comparison test and Limit Comparison test for series

1. Comparison test and Limit Comparison test for series

Hi, I don't know how to show that the series converges or diverges using the comparison test or limit comparison test. All the series so far have been rational.

Thanks in advance.

2. Originally Posted by witcon
Hi, I don't know how to show that the series converges or diverges using the comparison test or limit comparison test. All the series so far have been rational.

Thanks in advance.
Note that $\displaystyle \sqrt{n^4 + 1} - n^2 = \frac{1}{\sqrt{n^4 + 1} + n^2 }$.

3. What should I compare it with?

4. $\displaystyle \frac{1}{n^2}$

5. Originally Posted by witcon
What should I compare it with?
You are expected to note that $\displaystyle \frac{1}{\sqrt{n^4 + 1} + n^2} < \frac{1}{\sqrt{n^4} + n^2}$ ....

6. Which is also $\displaystyle < \frac{1}{n^2}$...