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Math Help - Couple of converge/diverge sequences.. Don't understand

  1. #1
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    Couple of converge/diverge sequences.. Don't understand



    For this one I did 3^((5+3n)/n) and I got the sequence converges to the square root of 27 and put that in but I was wrong.



    This one I did 2^n/9^n and I got that the sequence converges to 2/9 but I was wrong again.

    I don't understand why I am wrong.. Isn't this the correct way to solve it?
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  2. #2
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    \sqrt[n]{{3^{5 + 3n} }} = 27\sqrt[n]{{3^5 }}

    \dfrac{{2^{n + 6} }}{{9^n }} = 2^6 \left( {\dfrac{2}{9}} \right)^n
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  3. #3
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    As for the 2nd one shouldn't it be diverging?
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  4. #4
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    Quote Originally Posted by Reefer View Post
    As for the 2nd one shouldn't it be diverging?
    No indeed.
    What is the limit of \left( {\frac{2}{9}} \right)^n~?
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