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    Help please!!


    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!!
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    Divide through by the dominant term.
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    is 5^n the dominant term here? or n^5?
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    if i use 5^n I then the term 5(4^n) / 5^n isnt null!!
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    (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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