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# Converging sequences to a limit watch

Does this sequence converge and if so to what limit?
an = n^5 + 2(5^n) + 5(3^n) / n^3 + 3(5^n) - 5(4^n).

I would take 5^n as the dominant term but I am stuck!!
2. Divide through by the dominant term.
3. is 5^n the dominant term here? or n^5?
4. if i use 5^n I then the term 5(4^n) / 5^n isnt null!!
5. (Original post by Shaft284)
is 5^n the dominant term here? or n^5?
An exponential with a >1 base is dominant over any polynomial for large n.

(Original post by Shaft284)
if i use 5^n I then the term 5(4^n) / 5^n isnt null!!
Yes it is. If |q|<1 then q^n is a null sequence.

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Updated: December 30, 2012
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