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Math Help - Infinite Sequences

  1. #1
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    Infinite Sequences

    I'm hoping someone can help me out with a couple problems. For both of them, I need to determine if the sequence is convergent or divergent, and if it is convergent, I need to find the limit:

    1. a(sub n) = (5^n+2)/(7^n)

    2. a(sub n) = sqrt of (n+1)/(9n+1)

    Anyone have any ideas or suggestions??
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  2. #2
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    Quote Originally Posted by Jessica098 View Post
    I'm hoping someone can help me out with a couple problems. For both of them, I need to determine if the sequence is convergent or divergent, and if it is convergent, I need to find the limit:

    1. a(sub n) = (5^n+2)/(7^n)

    2. a(sub n) = sqrt of (n+1)/(9n+1)

    Anyone have any ideas or suggestions??
    1. Is it a_n = \frac{5^n + 2}{7^n} or a_n = \frac{5^{n + 2}}{7^n}\,?

    2. Note that \frac{n+1}{9n+1} = \frac{1 + \frac{1}{n}}{9 + \frac{1}{n}} .......
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    It's
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    Quote Originally Posted by Jessica098 View Post
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    Then a_n = 25 \, \left( \frac{5}{7} \right)^n ......

    (You know \lim_{n \rightarrow +\infty} \left( \frac{5}{7} \right)^n = 0, right?).
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  5. #5
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    Quote Originally Posted by Jessica098 View Post
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    Yes. I know. I read it the first time.

    Do you understand that 5^{n+2} = 5^n \times 5^2 = 5^n \times 25 = 25 (5^n) ? Now go back and read my previous reply again.
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    Quote Originally Posted by Jessica098 View Post
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    Perhaps it would be more efficient for you if, instead of simply repeating yourself, you told Mr. F. what exactly it is about his help you are not able to follow.

    -Dan
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