series convergence: sum [n=1, infty] [ -2 / (n sqrt[n]) ]

[cheffy]

\(\displaystyle \
\sum\limits_{n = 1}^\infty {\frac{{ - 2}}{{n\sqrt n }}}
\\)

How would I determine if this converges or diverges? I think I'm supposed to use an integer/p test since it's in that section of the book, but I don't see how I would.

Any suggestions?

Thanks!

 

[soroban]

Re: series convergence

Hello, cheffy!

Note that: \(\displaystyle \:n\cdot\sqrt{n} \:=\:n^{\frac{3}{2}}\)

 

[cheffy]

In order to use the integer/p test though, doesn't my function have to be positive decreasing? This function is negative increasing.

 

[skeeter]

Re: series convergence: sum [n=1, infty] [ -2 / (n sqrt[n])

\(\displaystyle \
-2 \sum\limits_{n = 1}^\infty \, {\frac{{1}}{{n^{\frac{3}{2}}}}
\\)