What series do I compare to when using the Limit Comparison test.
But that won't be sufficient, because for large n,
diverges, but the series in the original post consists of smaller terms, so you can't use that as a direct comparison. You can however, use the fact that
and the fact that the below diverges:
In fact the 2 in the above series can be ANY number greater than 1.
@SworD, you did not read the question carefully.
The question is about limit comparison not basic comparison.
Some authors like Gillman call it ratio comparison.
Yes, the (ordinary) comparison test is if where is a convergent series, then converges. Or if where is a divergent series, then diverges.
For the limit comparison test, if is finite and nonzero, then converges if and only if converges.
So you need to compare to 1/n, since is finite and nonzero. Of course, 1/2n or 35/87n would also work - the limits would still be finite and nonzero.
- Hollywood