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Math Help - Sequences and Series - Power Series Question

  1. #1
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    Unhappy Sequences and Series - Power Series Question

    Hey, i have a tonne of these type of questions and i cannot for the life of me understand how they are done....
    This is the answer to one of them which asks you to find the convergence and interval of convergence of the series: The sum from n=1 to infinity of the A(n) term at the start of the solution. I don't understand the step where they replace lim{[(n)/(n+1)]^3} with 1^3.

    Not sure if i grasp the concept of what to do ... can anyone explain?

    Thanks.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Schniz2 View Post
    Hey, i have a tonne of these type of questions and i cannot for the life of me understand how they are done....
    This is the answer to one of them which asks you to find the convergence and interval of convergence of the series: The sum from n=1 to infinity of the A(n) term at the start of the solution. I don't understand the step where they replace lim{[(n)/(n+1)]^3} with 1^3.

    Not sure if i grasp the concept of what to do ... can anyone explain?

    Thanks.
    Um, \lim_{n \to \infty} \frac n{n + 1} = 1

    there are many ways to see this. first you can realize that as n \to \infty, + 1 does not matter, so the fraction behaves like n/n = 1

    you could also realize that multiplying the numerator and denominator by 1/n yields \frac 1{1 + \frac 1n} which goes to 1 as n \to \infty, since \lim_{n \to \infty} \frac 1n = 0

    you can also use L'Hopital's rule. there are many ways to see this
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    Um, \lim_{n \to \infty} \frac n{n + 1} = 1

    there are many ways to see this. first you can realize that as n \to \infty, + 1 does not matter, so the fraction behaves like n/n = 1

    you could also realize that multiplying the numerator and denominator by 1/n yields \frac 1{1 + \frac 1n} which goes to 1 as n \to \infty, since \lim_{n \to \infty} \frac 1n = 0

    you can also use L'Hopital's rule. there are many ways to see this
    gosh, sometimes i wonder if i still have a brain. i've always suckes at limits and sequences.

    Thanks for that.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Schniz2 View Post
    gosh, sometimes i wonder if i still have a brain. i've always suckes at limits and sequences.

    Thanks for that.
    it is ok. i wonder the same thing about myself at times...
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