can anyone help me with converges/diverges problem?

Question

i know that diverges means that it is inf, goes on 4evr....
but if we find that a sequence converges, how do we calculate the sequence..for ex:
a(n)= { n^2 e^-6n}

Answer 1

Take the lim of x^2/e^6x by L´Hôpital = lim 2x/6e^6x= 2/36e^6x
=0 as e^6x ==> +infinity
so your sequence converges to zero