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Math Help - ratio test.

  1. #16
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dadon View Post
    by cancelling the 2n^2 and n^2 did i do it wrong?

    as you said they have to be product to cancel out?
    we had

    ......nē + 2n + 2 . . .2nē + 1
    . . .--------------- . .. ----------
    . . . . . . . . . . . . . .

    =
    ...nē/ + 2n/ + 2/ . ... .2nē/ + 1/
    . . .--------------------------- . .. ------------------
    . . . . ....... . nē/
    . . . . . .......... . .nē/

    =
    ...1 + 2/n + 2/ . ............... .2 + 1/
    . . .--------------------------- . .. ------------------
    . . . . ....... . 1
    . . . . . .......... ........ .1
    =
    (1 + 2/n + 2/nē)(2 + 1/)

    take the limit as n-->oo we get

    = (1 + 0 + 0)(2 + 0)
    = 2

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  2. #17
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    sorry I forgot to quote what I was asking

    here the question:

    (Un + 1) / (Un) = 1 + 2n^2 + 4n + 2 / 1 + n^2 + 2n + 1 . 1 + n^2 / 1 + 2n^2

    (Un + 1) / (Un) = 2n^2 + 4n + 3 / n^2 + 2n + 2 . 1 + n^2 / 1 + 2n^2

    cancelling out now to give: by cancelling the 2n^2 and n^2 did i do it wrong?

    (Un + 1) / (Un) = 4n + 3 / 2n + 2

    Lim n → ∞
    (Un + 1) / (Un) = 4 + (3/n) / 2 + (2/n)

    = 4 + 0 / 2 + 0

    = 2

    as > 1 series diverges.

    that's how I did it..
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  3. #18
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dadon View Post
    sorry I forgot to quote what I was asking

    here the question:

    (Un + 1) / (Un) = 1 + 2n^2 + 4n + 2 / 1 + n^2 + 2n + 1 . 1 + n^2 / 1 + 2n^2

    (Un + 1) / (Un) = 2n^2 + 4n + 3 / n^2 + 2n + 2 . 1 + n^2 / 1 + 2n^2

    cancelling out now to give: by cancelling the 2n^2 and n^2 did i do it wrong?

    (Un + 1) / (Un) = 4n + 3 / 2n + 2

    Lim n → ∞
    (Un + 1) / (Un) = 4 + (3/n) / 2 + (2/n)

    = 4 + 0 / 2 + 0

    = 2

    as > 1 series diverges.

    that's how I did it..
    yes, you're correct. you might want to work on your notation though. but i'm guilty of that as well
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