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Math Help - Adding and subtracting: Rational expressions

  1. #1
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    Adding and subtracting: Rational expressions

    Normally I wouldn't post the question straight out of the book, but today I am desperate because I just cannot get any bearing on this one.

    Triangular numbers of objects can be arranged to form triangles. The first four triangle numbers are: 1, 3, 6, 10.
    a)an expression to find the nth triangular number can be written in the form n(n+p)/q where p and q represent whole numbers. Complete the expression by determining the numbers represented by p and q.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mike_302 View Post
    Normally I wouldn't post the question straight out of the book, but today I am desperate because I just cannot get any bearing on this one.

    Triangular numbers of objects can be arranged to form triangles. The first four triangle numbers are: 1, 3, 6, 10.
    a)an expression to find the nth triangular number can be written in the form n(n+p)/q where p and q represent whole numbers. Complete the expression by determining the numbers represented by p and q.
    Well, the first triangular number is 1 so:

    1(1+p)/q=1

    and the second is 3, so:

    2(2+p)/q=3

    Hence:

    q-p=1

    and

    3q-2p=4

    so q=2, and p=1.

    Hence T_n=\frac{n(n+1)}{2}

    RonL
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  3. #3
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    Sorry, It was explained simply, and I like that, but you lost me at:

    Hence: q-p=1 ... I do not understand how you obtained that.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by mike_302 View Post
    Sorry, It was explained simply, and I like that, but you lost me at:

    Hence: q-p=1 ... I do not understand how you obtained that.
    The first equation I had was 1(1+p)/q=1, now assuming q \ne 0 this becomes on multiplying through by q:

    1+p=q

    which is then rearranged to give q-p=1

    RonL
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