I need to show if the following sequence converges and its limit.

3n^2+4^n+2^n/n^23^n+4n^7

The dominant term is 4^n.

Dividing both numerator and denominator by 4^n, we get

3n^2/4^n + 1 + (2/4)^n / n^2(3/4)^n + 4n^7/4^n

Since n^2/4^n, (2/4)^n, n^2(3/4)^n and n^7/4^n are basic null sequences, we find, by the combination rules, that

lim = 0+1+0/0+0 = ?

not sure what to do. Can anyone help?