test for convergence

[iDoof]

what test should i use for this infinite series?

SUM (from n=1 to infinity) of (n*ln n)/((n+1)^3)

should i use the p-test?


thanks a lot!!

 

[pka]

For every x>1, ln(x)<x.
The ln(√n)=(1/2)ln(n) or ln(n)<2√n.
Now n*ln(n)< 2(n)<SUP>3/2</SUP>.
Using basic comparison and the p-test you can finish this off.