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Determine whether the sequences are increasing

  • #1

Homework Statement


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]

Homework Equations





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.
 

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