Use what test?

a) ∑(from n=1 to infinity) (arctan n/ n^1.2)

b) ∑(from n=1 to infinity) ( (n^n) / (2n)! )

Not sure how to do these...when i do it using ratio test, it turns out really weird..so yea i need help.

Thanks.

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- May 21st 2008, 01:05 AMRuiSeries converge or diverge?
**Use what test?**

a) ∑(from n=1 to infinity) (arctan n/ n^1.2)

b) ∑(from n=1 to infinity) ( (n^n) / (2n)! )

Not sure how to do these...when i do it using ratio test, it turns out really weird..so yea i need help.

Thanks. - May 21st 2008, 01:23 AMflyingsquirrel
- May 21st 2008, 01:49 AMangel.white
Comparison test:

let , and let

Then (because )

And is a p-series with p=1.2, which is greater than 1, therefore converges, and because is monotonic and increasing, and bounded above by we know that converges by the comparison test.

Ratio Test:

, and

Here multiply numerator and denominator by 1 over n^n to get

Now multiply the numerator and denominator by 1/n to get

It should be relatively clear that this converges to zero, (because the numerator converges to e, and the denominator diverges) but if you need me to explain that more, I can.

So because the series is absolutely convergent and therefore convergent. - May 21st 2008, 03:23 AMMathstud28
- June 1st 2008, 08:12 AMMathstud28