Does the series converge or diverge?:
sum of (-1)^n * ln(n)/n^(1/2)

Question

Does the series converge or diverge?:
sum of  (-1)^n * ln(n)/n^(1/2)

anonymous · Answer

What's the limit as $n\to\infty$?

paxpolaris · Answer

$$\sum \left( -1 \right)^n {\ln \left( n \right) \over \sqrt n}$$

anonymous · Answer

the lim as n goes to infinity is
$$\lim_{n \rightarrow \infty} \left| (-1)^n*\frac{ \ln(n) }{ n^(\frac{ 1 }{ 2 }) } \right|$$

I started it out trying to do it with the root test, but I got stuck...

anonymous · Answer

Have you learned about the alternating series test yet?

anonymous · Answer

I have... Ill try that really quick

anonymous · Answer

HI... I have a different way. Will you like to know?. @kreimer20 ?

anonymous · Answer

yes please? I don't mind learning another way

anonymous · Answer

oh, i thought it is n^2 in the denominator.. Hmm ok you try Leibnitz's method, let me see if i can get any easy approach or not.

anonymous · Answer

Ok i got an easy method...

anonymous · Answer

lim (ln n)/n^(1/2)=0 and lim ln(n+1)/(n+1)^(1/2)=0 we can say that the series of even terms and odd terms converges to 0, And hence the series converges to 0

anonymous · Answer

@kreimer20

anonymous · Answer

I'm not too worried about finding out what it converges to.. I think my professor wants us using certain methods in this... so I did it with the alternating series and got it converging... so thanks anyway!

anonymous · Answer

@kreimer20 keep in mind that you might need to say something about conditional vs absolute convergence.