calculus BC help

[encipher]

How would you figure out if this converges or diverges: 1/((n)(lnn)^2)

[Klaynos]

There are a few methods I belive. One of which is the Newton–Raphson method. I recall (from several years ago) that this is the most mathematically heavy but most likely to work method...

 

http://en.wikipedia.org/wiki/Newton's_method

 

Have fun.

[Dave]

I'm going to assume that you mean the sequence:

 

[math](a_n)_{n=1}^{\infty} = \frac{1}{n \log^2 n}[/math]

 

instead of the continuous function. But the same principle should apply, I think. You should notice that, for [imath]n \geq 2[/imath], [imath]0 \leq \frac{1}{n} \leq 1[/imath]. So,

 

[math]0 \leq \frac{1}{n \log^2 n} \leq \frac{1}{\log^2 n}[/math]

 

The rest should be obvious.