- #1
miglo
- 98
- 0
Homework Statement
[tex]\sum_{n=2}^{\infty}\frac{1}{n\sqrt{n^2-1}}[/tex]
Homework Equations
direct comparison test
limit comparison test
The Attempt at a Solution
so i kind of cheated and looked at the back of my book and it says to compare with [itex]\frac{1}{n^{3/2}}[/itex]
so i tried using the direct comparison test and tried to show that the original series converges if [tex]\frac{1}{n\sqrt{n^2-1}}<\frac{1}{n^{3/2}}[/tex] since [tex]\sum_{n=1}^{\infty}\frac{1}{n^{3/2}}[/tex] is a convergent p-series test
i just don't know how to actually show [tex]\frac{1}{n\sqrt{n^2-1}}<\frac{1}{n^{3/2}}[/tex]
or am i using the wrong test? limit comparison? by the way the only tests I've covered in my class are the divergence, p-series, integral, direct comparison, limit comparison tests and geometric and telescoping series
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