Hi, its me again

I got some problems with limit of the series and sequence and here are the question I'm not so sure about and got stuck with.

The first question is

Consider for n morethanorequalto 1, the sequence {a_{n}} given by a_{n}= n x IN(n/(n-1))

Determine the limit as n approach infinity, if it exists or explain why the sequence diverges.

a_{n}= n x IN(n/(n-1))

= lim(n approach infinity) n x lim(n approach infinity) IN(n/(n-1) (IN is for log based e)

= lim(n approach infinity) n x lim(n approach infinity) IN (1/(1-(1/n))

since n approach infinity 1/n will become very small

= lim(n approach infinity) n x lim(n approach infinity) IN(1/1)

= lim(n approach infinity) n x 0

= 0

The answer I have is that the limit of this sequence is equal to 0. Is this correct?

The second question is

Using an appropriate test, determine whether the following series is convergent or divergent

ZIGMA (with infinity on top of it) and n=1 under it (ZIGMA as in series). Zigma ((n!)^3 /(3n)!)

I do not know how to do the second question. So if any one can explain to me I'll be eternally grateful until the day I died

Best Regards

Junks

I'm very sorry that I do not know how to do the nice mathematics expression.