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Math Help - Sequences Question Please Help

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    Sequences Question Please Help

    ok i have this problem in the textbook where An= 3^(n+2)/5^n and i am suppose to determine whether it converges or diverges and if it convergies i have to find the limit... any ideals how to do this?
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    Quote Originally Posted by Krebs View Post
    ok i have this problem in the textbook where An= 3^(n+2)/5^n and i am suppose to determine whether it converges or diverges and if it convergies i have to find the limit... any ideals how to do this?
    Try re-writing your problem as

    A_n = \frac{3^n 3^2}{5^n} = 9 \left( \frac{3}{5} \right)^n. To show it converges show (i) it's decreasing and (ii) bounded below by 0.
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    Quote Originally Posted by danny arrigo View Post
    Try re-writing your problem as

    A_n = \frac{3^n 3^2}{5^n} = 9 \left( \frac{3}{5} \right)^n. To show it converges show (i) it's decreasing and (ii) bounded below by 0.

    ok so that means that as n approaches infinity An approaches 0 since An is getting smaller and smaller as n gets larger? and thank you for your help
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    Quote Originally Posted by Krebs View Post
    ok so that means that as n approaches infinity An approaches 0 since An is getting smaller and smaller as n gets larger? and thank you for your help
    Yes. More formally you want to show (for decreasing)

    A_{n+1} < A_n

    I think that A_n >0 is obvious.
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