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Did i do the reduction correctly? algebra type stuff!

  1. Mar 9, 2006 #1
    Directions:
    Find all the values of x such that the given series would converge.

    [​IMG]
    Here is my work:
    [​IMG]

    I got it wrong but is it because i don't know how to do inequalities, or just suck in general?
     
  2. jcsd
  3. Mar 9, 2006 #2
    What happened to the 2?

    -Dan
     
  4. Mar 9, 2006 #3
    I follow you until this line: [tex]\lim_{n\rightarrow\infty}\frac{(-x)(n^2+3)}{2n^2+4n+8}[/tex]

    and then I don't see what you're doing.
     
  5. Mar 9, 2006 #4
    Okay from here, i'm using the rule, where u divide by the largest exponent, in this case its n^2, so u divide every term by n^2 and leave the -x alone, then u take as n->infinity. I'm using this website as my guide:
    http://www.math.unh.edu/~jjp/radius/radius.html

    Ooo i don't know where the 2 went lol i will do it again with the 2
     
  6. Mar 9, 2006 #5
    Sweet it worked once i added the 2 lol.

    |-x|/2 < 1

    |-x| < 2
    -2 < x <2

    quick question though. is |-x| == |x|? i just assumed it was, thats how i came out with -2 < x < 2
     
  7. Mar 9, 2006 #6
    I was wondering why you didn't just go straight to |x|/2. And yes, I think you're answer is correct.
     
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