Thank you both. That helped a lot. I used the comparison test and the p-series test and it does converge.
The real problem was similar in that instead of \sqrt{k^{2}+1} - \sqrt{k^{2}} it was \sqrt{k^{5}+10} - \sqrt{k^{5}}. I just didn't want it to feel like cheating. Thanks again.
1. \sum(\sqrt{k^{2}+1}-\sqrt{k^{2}}) from K=0 to K=\infty
2. Hi all. I need some help here. I have to use a test to determine whether the sum series diverges or converges
3. I thought it was the divergence test because I thought that the limit of the sum didn't approach zero...