Find the radius of convergence and interval of convergence of the series

$\displaystyle \sum_{n=2}^{\infty}\frac{x^{2n}}{n(lnn)^2}$

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- Mar 1st 2010, 06:51 PMEm Yeu AnhInfinite series problem
Find the radius of convergence and interval of convergence of the series

$\displaystyle \sum_{n=2}^{\infty}\frac{x^{2n}}{n(lnn)^2}$ - Mar 1st 2010, 07:24 PMTKHunny
What were your conculsions from the Ratio Test?

- Mar 1st 2010, 07:45 PMEm Yeu Anh
$\displaystyle \lim_{n\to\infty}|\frac{x^{2n+2}}{(n+1)(ln(n+1))^2 }*\frac{n(lnn)^2}{x^{2n}}|$

= $\displaystyle \lim_{n\to\infty}|x^2(\frac{n}{n+1})\frac{(lnn)^2} {(ln(n+1))^2}$

It's simplifying the natural logarithms that I am a bit confused with (hopefully I did not make an error yet) sorry, I should have specified that earlier. - Mar 2nd 2010, 08:02 AMTKHunny
Well, that was the

**application**of the Ratio Test.

You did not make any**conclusion**.

Why do you require simplification? Let's draw some conclusions without it. It looks to me like just about every piece is approaching unity. Where does that leave us?

Note: Nice screen name. I wish more folks felt that way about mathematics! (Clapping) Why do you hoist a China flag and speak from Viet Nam?

Other Note: From your experience, does whatever culture you know tell women and girls that they can't do math? Obviously, that would be a silly thing to tell**you**, but it may remain a common cultural message.