What series do I compare to when using the Limit Comparison test.

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- Dec 20th 2012, 01:39 PMMSUMathStdntLimit Comparison Test of the series of sin(1/n)
What series do I compare to when using the Limit Comparison test.

- Dec 20th 2012, 01:44 PMPlatoRe: Limit Comparison Test of the series of sin(1/n)
- Dec 20th 2012, 02:27 PMSworDRe: Limit Comparison Test of the series of sin(1/n)
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. - Dec 20th 2012, 02:46 PMPlatoRe: Limit Comparison Test of the series of sin(1/n)

@SworD,**you did not read the question carefully**.

The question is aboutnot basic comparison.__limit__comparison

Some authors like Gillman call it*ratio comparison*.

- Dec 20th 2012, 08:13 PMhollywoodRe: Limit Comparison Test of the series of sin(1/n)
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