Woo boy, second day in calculus class. It is serious business here.

Okay, we reviewed on series and sequences, and briefly touched on recursives. Now we’re doing limits on serieses. Help needed for the question below:

<b>t</b><i>n</i> = the <i>n</i>th root of <i>n</i>

Using the above equation of the series, I had to find <b>t</b><i>n</i> if <i>n</i> equals 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 50, 100, 500, 1000, and 10 000.

I do so, easy stuff.

Then it says:

lim <i>n</i>—> ∞

That applies to the equation of the series which was given: <b>t</b><i>n</i> = the <i>n</i>th root of <i>n</i>. I know what it means and all.

But how would I find the limit? I’m guessing it’s zero.

According to this sheet the instructor handed out; stating three rules about limit:

(I omitted the “Lim n–>∞” thing, 'cause it’s too long to put in, but assume it’s infront of each of the equations below)

R.1: 1/<i>n</i>^<u>r</u> , if <u>r</u> > 0 , then it equals 0.

R.2: <u>r</u>^<i>n</i> , if |r| (what does this mean?) < 1 , then it also requals 0.

R.3: |<u>r</u>^<i>n</i>| , if |r| > 1 , then it equals ∞.

But, it doesn’t state anything about roots.

Thanks for your help.