Series converges? or diverges? Which test? explain?
(n^10) * (3^n)
------------(fraction)
(4^n)
from n=1 to infinity
The terms of the sequence are
(3/4)^n * n^10
or,
n^10 / (4/3)^n
I'm sure you've seen proofs that exponentials grow faster than polynomials, so this limit --> 0
a google search will turn up many proofs of this, such as
http://math.stackexchange.com/questions/55468/how-to-prove-that-exponential-grows-faster-than-polynomial
or, you can apply l'Hospital's Rule several times till the numerator goes to zero while the denominator does not.