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Thread: 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 $\displaystyle 1$ so:

    $\displaystyle 1(1+p)/q=1$

    and the second is $\displaystyle 3$, so:

    $\displaystyle 2(2+p)/q=3$

    Hence:

    $\displaystyle q-p=1$

    and

    $\displaystyle 3q-2p=4$

    so $\displaystyle q=2$, and $\displaystyle p=1$.

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

    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 $\displaystyle 1(1+p)/q=1$, now assuming $\displaystyle q \ne 0$ this becomes on multiplying through by $\displaystyle q$:

    $\displaystyle 1+p=q$

    which is then rearranged to give $\displaystyle q-p=1$

    RonL
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