Is the limit:
?
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?