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Math Help - Series

  1. #1
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    Series

    Determine whether the series is convergent or divergent. If it is convergent, find its sum.

    1) Sum of k(k+2) / (k+3)^2 with k = 1 to infinity.

    2) Sum of (cos 1)^k with k = 1 to infinity.

    can someone help me with these? thanks.
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  2. #2
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    For #1 apply the first test for convergence: \left( {a_n } \right) \to 0???

    For #2, How large is cos(1)?
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xfyz View Post
    Determine whether the series is convergent or divergent. If it is convergent, find its sum.

    1) Sum of k(k+2) / (k+3)^2 with k = 1 to infinity.
    this sum diverges to infinity.

    2) Sum of (cos 1)^k with k = 1 to infinity.

    can someone help me with these? thanks.
    i don't know i believe it is convergent though, but it may not be, the reverse implication of the theorem Plato hinted at is not always true


    EDIT: Ah, i do know. it's a geometric series. finally got Plato's hint...stupid me
    Last edited by Jhevon; October 28th 2007 at 05:34 PM.
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  4. #4
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    Quote Originally Posted by Plato View Post
    For #1 apply the first test for convergence: \left( {a_n } \right) \to 0???

    For #2, How large is cos(1)?
    For the 1st one, i think the book wants me to use the ar^n-1 method ?
    In your reply, are you telling me to just take the limit as n goes to infinity of that equation?

    2) what do u mean how large is cos 1 ? cos 1 is close to .5 .. am i supposed to consider the domain? -1 > x > 1 ?
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xfyz View Post
    For the 1st one, i think the book wants me to use the ar^n-1 method ?
    In your reply, are you telling me to just take the limit as n goes to infinity of that equation?
    yes, take the limit of the formula
    2) what do u mean how large is cos 1 ? cos 1 is close to .5 .. am i supposed to consider the domain? -1 > x > 1 ?
    his point is, it's a convergent geometric sequence.

    ah, there's the answer! find the formula for the sum of a geometric series
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  6. #6
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    Quote Originally Posted by Jhevon View Post
    yes, take the limit of the formula
    his point is, it's a convergent geometric sequence.

    ah, there's the answer! find the formula for the sum of a geometric series
    a / 1-r

    cos 1 / 1 - cos 1 = 1.175

    is this correct?
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xfyz View Post
    a / 1-r

    cos 1 / 1 - cos 1 = 1.175

    is this correct?
    yes
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