Converge/Diverge help

**Krebs** · February 9th 2009, 11:47 AM

I have to determine whether these series converge or diverge and i got stuck on 2 of them

the first one is 1/ (n) (squareroot n)

and the second one is n-1/(n^2) (squareroot n)

any idelas how to do either of these two?
Thanks

**Krizalid** · February 9th 2009, 11:57 AM

$\sum\limits_{n=1}^{\infty }{\frac{1}{n\sqrt{n}}}=\sum\limits_{n=1}^{\infty }{\frac{1}{{{n}^{3/2}}}}<\infty ,$ 'cause it's a convergent $p-$ series with $p=\frac32>1.$

For your second question, $\sum\limits_{n=2}^{\infty }{\frac{n-1}{{{n}^{2}}\sqrt{n}}}\le \sum\limits_{n=2}^{\infty }{\frac{n}{{{n}^{2}}\sqrt{n}}}=\sum\limits_{n=2}^{ \infty }{\frac{1}{n\sqrt{n}}}<\infty,$ convergent by the above reason.

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