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Determine whether the sequences are increasing

  1. Nov 4, 2007 #1
    1. The problem statement, all variables and given/known data
    Determine whether the sequences are increasing, decreasing, or not monotonic.
    1) an= [tex]\frac{\sqrt{n+2}}{4n+2}[/tex]
    2) an=[tex]\frac{1}{4n+2}[/tex]
    3) an=[tex]\frac{cosn}{2^{n}}[/tex]
    4) an=[tex]\frac{n-2}{n+2}[/tex]
    2. Relevant equations

    3. The attempt at a solution
    I thought that the number 1 and 2 were decreasing because [tex]a_{n}[/tex] [tex]\geq[/tex] [tex]a_{n+1}[/tex] in both cases
    #3 is increasing because [tex]a_{n}[/tex][tex]\leq[/tex] [tex]a_{n+1}[/tex]
    #4 is monotonic because if n=3 then its 0

    for number #1 I compared it to [tex]a_{n+1}[/tex]=[tex]\frac{\sqrt{n+3}}{4n+6}[/tex]
    and i found that it was smaller than an so it was decreasing
    i did this procedure for the rest of them and i still get the wrong answer
    can someone please help me.
  2. jcsd
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