what tests have you learnt so far. let's try the comparison test, i think that's the easiest way to do this.E (1/(ln(n)).
note that 1/n < 1/ln(n) .........since n is larger than ln(n) for all n
so E 1/n < E 1/ln(n)
now since E 1/n diverges, E 1/ln(n) diverges by the comparison test