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Math Help - convergence of sequence

  1. #1
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    convergence of sequence

    For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

    A) Sn = ( (-1)^n / (n+3) )
    B) Sn = ( 2^(3n) / 3^(2n) )
    C) Sn = ( (3+n-n^2) / (1+2n) )
    D) Sn = 3^n / (n^3 + 5)
    E) Sn = n! / (n^n)
    F) Sn = (n^2) / n!
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  2. #2
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    Is this confusing just as much to others as is to me?
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  3. #3
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    No, it is not at all confusing. What have you tried?
    What donít you understand about these?
    They are rather standard and simple sequences.

    Do you see that (b) is no more than (8/9)^n?
    What do you know about (r^n) if |r|<1 ?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by luckyc1423 View Post
    For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

    A) Sn = ( (-1)^n / (n+3) )
    Here
    Attached Thumbnails Attached Thumbnails convergence of sequence-converge1.gif  
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by luckyc1423 View Post
    For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

    B) Sn = ( 2^(3n) / 3^(2n) )
    Here
    Attached Thumbnails Attached Thumbnails convergence of sequence-converge2.gif  
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by luckyc1423 View Post
    For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

    C) Sn = ( (3+n-n^2) / (1+2n) )
    Here
    Attached Thumbnails Attached Thumbnails convergence of sequence-converge3.gif  
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by luckyc1423 View Post
    For Sn given by the following formulas, determine the convergence or divergence of the sequence (Sn). Find any limits that exist:

    D) Sn = 3^n / (n^3 + 5)
    Here
    Attached Thumbnails Attached Thumbnails convergence of sequence-converge4.gif  
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