Results 1 to 6 of 6

Thread: Does the fraction simplify?

  1. #1
    Junior Member
    Joined
    Mar 2011
    Posts
    32

    Does the fraction simplify?

    Hi all,

    I've been doing well all year, but now I've hit a wall. All the exercises prior to this question have had just one term of n, but now this has shown it's ugly self, and I am absolutely confused.

    The question regards sequences;

    For the sequence below, decide whether it converges and, if it does, state its limit.

    a(term n) = 6n^4 + 2n^3 (which is all over) 7n - 11n^4 (n=1,2,3,...)

    if the fraction simplifies so I can get either the numerator or the denominator a constant with no terms of n in, I should be OK then.

    Any help would be great.

    Shayne.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    10
    Quote Originally Posted by Hydralisk View Post
    Hi all,

    I've been doing well all year, but now I've hit a wall. All the exercises prior to this question have had just one term of n, but now this has shown it's ugly self, and I am absolutely confused.

    The question regards sequences;

    For the sequence below, decide whether it converges and, if it does, state its limit.

    a(term n) = 6n^4 + 2n^3 (which is all over) 7n - 11n^4 (n=1,2,3,...)

    if the fraction simplifies so I can get either the numerator or the denominator a constant with no terms of n in, I should be OK then.

    Any help would be great.

    Shayne.
    For fractions like this, the technique is to divide top and bottom by the highest power of n in sight (in this case, n^4), and use the fact that negative powers of n go to zero as n\to\infty.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2011
    Posts
    32
    That's helped, but I've still got terms of n in both the numerator and the denominator, so it's still "hard" for me.

    I've now got:

    (2/n)+ 6 (all over) (7/n^3)-11

    is there anything I can do to get rid of the (2/n) in the numerator maybe?

    Many thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    10
    Quote Originally Posted by Hydralisk View Post
    That's helped, but I've still got terms of n in both the numerator and the denominator, so it's still "hard" for me.

    I've now got:

    (2/n)+ 6 (all over) (7/n^3)-11

    is there anything I can do to get rid of the (2/n) in the numerator maybe?

    Many thanks.
    You just need to see that 2/n and 7/n^3 both get smaller and smaller as n increases. In the limit, they both tend to 0 (so you can ignore them altogether), and the fraction becomes 6/(–11) (which is the answer to the question).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2011
    Posts
    32
    Hi,

    many thanks to you both, I did infact write down 6/-11 after a bit of time thinking it through, but having it confirmed is such a releif.

    Thanks again.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    4
    Another way to think it through is.....

    As "n" approaches infinity, 6n^4 will dwarf 2n^3

    and -11n^4 will dwarf 7n

    so your fraction approaches

    \displaystyle-\frac{6n^4}{11n^4}=-\left(\frac{n^4}{n^4}\right)\frac{6}{11}=-\frac{6}{11}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simplify fraction
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Nov 22nd 2008, 09:06 AM
  2. simplify fraction
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 15th 2008, 07:16 PM
  3. Simplify fraction.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Feb 8th 2008, 02:19 PM
  4. Simplify the fraction
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Dec 11th 2007, 11:40 AM
  5. simplify fraction
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Mar 4th 2007, 03:47 PM

Search Tags


/mathhelpforum @mathhelpforum